10 94

10_93

10_95

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10 94 Further Notes and Views

Knot presentations

Planar diagram presentation	X6271 X2837 X18,12,19,11 X14,5,15,6 X20,14,1,13 X8,15,9,16 X10,4,11,3 X16,9,17,10 X4,17,5,18 X12,20,13,19
Gauss code	1, -2, 7, -9, 4, -1, 2, -6, 8, -7, 3, -10, 5, -4, 6, -8, 9, -3, 10, -5
Dowker-Thistlethwaite code	6 10 14 2 16 18 20 8 4 12
Conway Notation	[.30.2.2]

Minimum Braid Representative: Length is 10, width is 3. Braid index is 3.

A Morse Link Presentation:

Three dimensional invariants

Symmetry type Chiral Unknotting number 2 3-genus 4 Bridge index 3 Super bridge index Missing Nakanishi index 1 Maximal Thurston-Bennequin number [-3][-9] Hyperbolic Volume 13.3116 A-Polynomial See Data:10 94/A-polynomial

[edit Notes for 10 94's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus $1$ Topological 4 genus $1$ Concordance genus $4$ Rasmussen s-Invariant -2

[edit Notes for 10 94's four dimensional invariants]

Polynomial invariants

Alexander polynomial	$-t^{4}+4t^{3}-9t^{2}+14t-15+14t^{-1}-9t^{-2}+4t^{-3}-t^{-4}$
Conway polynomial	$-z^{8}-4z^{6}-5z^{4}-2z^{2}+1$
2nd Alexander ideal (db, data sources)	$\{1\}$
Determinant and Signature	{ 71, 2 }
Jones polynomial	$q^{7}-3q^{6}+6q^{5}-9q^{4}+11q^{3}-12q^{2}+11q-8+6q^{-1}-3q^{-2}+q^{-3}$
HOMFLY-PT polynomial (db, data sources)	$-z^{8}a^{-2}-6z^{6}a^{-2}+z^{6}a^{-4}+z^{6}-13z^{4}a^{-2}+4z^{4}a^{-4}+4z^{4}-12z^{2}a^{-2}+5z^{2}a^{-4}+5z^{2}-4a^{-2}+2a^{-4}+3$
Kauffman polynomial (db, data sources)	$2z^{9}a^{-1}+2z^{9}a^{-3}+9z^{8}a^{-2}+5z^{8}a^{-4}+4z^{8}+3az^{7}+3z^{7}a^{-3}+6z^{7}a^{-5}+a^{2}z^{6}-27z^{6}a^{-2}-9z^{6}a^{-4}+5z^{6}a^{-6}-12z^{6}-9az^{5}-11z^{5}a^{-1}-15z^{5}a^{-3}-10z^{5}a^{-5}+3z^{5}a^{-7}-3a^{2}z^{4}+31z^{4}a^{-2}+10z^{4}a^{-4}-6z^{4}a^{-6}+z^{4}a^{-8}+11z^{4}+6az^{3}+10z^{3}a^{-1}+16z^{3}a^{-3}+9z^{3}a^{-5}-3z^{3}a^{-7}+2a^{2}z^{2}-18z^{2}a^{-2}-6z^{2}a^{-4}+2z^{2}a^{-6}-z^{2}a^{-8}-7z^{2}-az-3za^{-1}-5za^{-3}-3za^{-5}+4a^{-2}+2a^{-4}+3$
The A2 invariant	$q^{8}-q^{6}+2q^{4}+1+2q^{-2}-3q^{-4}+2q^{-6}-3q^{-8}+q^{-10}-q^{-14}+2q^{-16}-q^{-18}+q^{-20}$
The G2 invariant	$q^{46}-2q^{44}+5q^{42}-9q^{40}+10q^{38}-9q^{36}+17q^{32}-34q^{30}+51q^{28}-55q^{26}+35q^{24}+5q^{22}-60q^{20}+111q^{18}-124q^{16}+97q^{14}-28q^{12}-55q^{10}+125q^{8}-149q^{6}+116q^{4}-36q^{2}-49+109q^{-2}-110q^{-4}+59q^{-6}+24q^{-8}-87q^{-10}+112q^{-12}-89q^{-14}+15q^{-16}+69q^{-18}-141q^{-20}+167q^{-22}-135q^{-24}+54q^{-26}+49q^{-28}-143q^{-30}+185q^{-32}-173q^{-34}+99q^{-36}-95q^{-40}+144q^{-42}-127q^{-44}+62q^{-46}+25q^{-48}-86q^{-50}+94q^{-52}-53q^{-54}-19q^{-56}+84q^{-58}-110q^{-60}+97q^{-62}-39q^{-64}-29q^{-66}+84q^{-68}-109q^{-70}+99q^{-72}-63q^{-74}+18q^{-76}+23q^{-78}-53q^{-80}+65q^{-82}-58q^{-84}+44q^{-86}-20q^{-88}-2q^{-90}+17q^{-92}-28q^{-94}+26q^{-96}-19q^{-98}+11q^{-100}-2q^{-102}-3q^{-104}+5q^{-106}-6q^{-108}+4q^{-110}-2q^{-112}+q^{-114}$

Further Quantum Invariants

Further quantum knot invariants for 10_94.

A1 Invariants.

Weight	Invariant
1	$q^{7}-2q^{5}+3q^{3}-2q+3q^{-1}-q^{-3}-q^{-5}+2q^{-7}-3q^{-9}+3q^{-11}-2q^{-13}+q^{-15}$
2	$q^{22}-2q^{20}-q^{18}+8q^{16}-4q^{14}-11q^{12}+15q^{10}+3q^{8}-22q^{6}+12q^{4}+15q^{2}-21+3q^{-2}+18q^{-4}-12q^{-6}-8q^{-8}+12q^{-10}+5q^{-12}-14q^{-14}-2q^{-16}+21q^{-18}-12q^{-20}-15q^{-22}+23q^{-24}-4q^{-26}-15q^{-28}+13q^{-30}-7q^{-34}+5q^{-36}-2q^{-40}+q^{-42}$
3	$q^{45}-2q^{43}-q^{41}+4q^{39}+5q^{37}-7q^{35}-16q^{33}+8q^{31}+32q^{29}+3q^{27}-47q^{25}-30q^{23}+56q^{21}+63q^{19}-43q^{17}-98q^{15}+9q^{13}+117q^{11}+36q^{9}-116q^{7}-76q^{5}+94q^{3}+110q-61q^{-1}-123q^{-3}+31q^{-5}+123q^{-7}-q^{-9}-117q^{-11}-20q^{-13}+99q^{-15}+46q^{-17}-81q^{-19}-69q^{-21}+51q^{-23}+91q^{-25}-11q^{-27}-109q^{-29}-35q^{-31}+113q^{-33}+79q^{-35}-96q^{-37}-111q^{-39}+64q^{-41}+122q^{-43}-28q^{-45}-106q^{-47}-3q^{-49}+77q^{-51}+17q^{-53}-45q^{-55}-16q^{-57}+20q^{-59}+9q^{-61}-9q^{-63}-2q^{-65}+6q^{-67}-2q^{-69}-3q^{-71}+q^{-73}+2q^{-75}-2q^{-79}+q^{-81}$
4	$q^{76}-2q^{74}-q^{72}+4q^{70}+q^{68}+2q^{66}-13q^{64}-10q^{62}+17q^{60}+22q^{58}+29q^{56}-41q^{54}-79q^{52}-18q^{50}+60q^{48}+164q^{46}+38q^{44}-156q^{42}-215q^{40}-101q^{38}+278q^{36}+340q^{34}+67q^{32}-328q^{30}-527q^{28}-29q^{26}+471q^{24}+589q^{22}+79q^{20}-698q^{18}-636q^{16}+12q^{14}+791q^{12}+756q^{10}-240q^{8}-880q^{6}-681q^{4}+394q^{2}+1041+402q^{-2}-578q^{-4}-980q^{-6}-138q^{-8}+824q^{-10}+691q^{-12}-177q^{-14}-848q^{-16}-380q^{-18}+499q^{-20}+668q^{-22}+41q^{-24}-627q^{-26}-454q^{-28}+244q^{-30}+638q^{-32}+245q^{-34}-415q^{-36}-611q^{-38}-139q^{-40}+587q^{-42}+625q^{-44}+22q^{-46}-736q^{-48}-738q^{-50}+229q^{-52}+902q^{-54}+693q^{-56}-433q^{-58}-1120q^{-60}-423q^{-62}+624q^{-64}+1076q^{-66}+207q^{-68}-836q^{-70}-766q^{-72}-10q^{-74}+770q^{-76}+534q^{-78}-215q^{-80}-501q^{-82}-324q^{-84}+222q^{-86}+341q^{-88}+90q^{-90}-104q^{-92}-211q^{-94}-20q^{-96}+81q^{-98}+61q^{-100}+34q^{-102}-55q^{-104}-19q^{-106}-3q^{-108}+2q^{-110}+23q^{-112}-8q^{-114}+q^{-116}-2q^{-118}-5q^{-120}+5q^{-122}-2q^{-124}+2q^{-126}-2q^{-130}+q^{-132}$
5	$q^{115}-2q^{113}-q^{111}+4q^{109}+q^{107}-2q^{105}-4q^{103}-7q^{101}-2q^{99}+20q^{97}+29q^{95}+3q^{93}-35q^{91}-70q^{89}-57q^{87}+29q^{85}+153q^{83}+182q^{81}+47q^{79}-189q^{77}-377q^{75}-304q^{73}+77q^{71}+555q^{69}+716q^{67}+315q^{65}-473q^{63}-1126q^{61}-1045q^{59}-73q^{57}+1238q^{55}+1851q^{53}+1128q^{51}-637q^{49}-2308q^{47}-2492q^{45}-736q^{43}+1933q^{41}+3540q^{39}+2665q^{37}-437q^{35}-3709q^{33}-4540q^{31}-1916q^{29}+2582q^{27}+5605q^{25}+4549q^{23}-253q^{21}-5375q^{19}-6677q^{17}-2714q^{15}+3787q^{13}+7675q^{11}+5543q^{9}-1226q^{7}-7321q^{5}-7597q^{3}-1582q+5857q^{-1}+8459q^{-3}+3990q^{-5}-3761q^{-7}-8193q^{-9}-5571q^{-11}+1674q^{-13}+7126q^{-15}+6149q^{-17}-10q^{-19}-5670q^{-21}-5959q^{-23}-1021q^{-25}+4337q^{-27}+5278q^{-29}+1421q^{-31}-3286q^{-33}-4535q^{-35}-1499q^{-37}+2679q^{-39}+4036q^{-41}+1513q^{-43}-2314q^{-45}-3909q^{-47}-1884q^{-49}+1935q^{-51}+4143q^{-53}+2769q^{-55}-1183q^{-57}-4446q^{-59}-4162q^{-61}-249q^{-63}+4388q^{-65}+5821q^{-67}+2395q^{-69}-3569q^{-71}-7183q^{-73}-4998q^{-75}+1740q^{-77}+7677q^{-79}+7530q^{-81}+910q^{-83}-6921q^{-85}-9239q^{-87}-3829q^{-89}+4883q^{-91}+9579q^{-93}+6295q^{-95}-2085q^{-97}-8438q^{-99}-7586q^{-101}-702q^{-103}+6134q^{-105}+7465q^{-107}+2787q^{-109}-3470q^{-111}-6159q^{-113}-3707q^{-115}+1141q^{-117}+4233q^{-119}+3573q^{-121}+401q^{-123}-2380q^{-125}-2774q^{-127}-1047q^{-129}+987q^{-131}+1771q^{-133}+1086q^{-135}-177q^{-137}-952q^{-139}-819q^{-141}-142q^{-143}+408q^{-145}+490q^{-147}+214q^{-149}-121q^{-151}-261q^{-153}-163q^{-155}+16q^{-157}+108q^{-159}+92q^{-161}+23q^{-163}-38q^{-165}-49q^{-167}-17q^{-169}+16q^{-171}+14q^{-173}+6q^{-175}+2q^{-177}-7q^{-179}-5q^{-181}+3q^{-183}+2q^{-185}-2q^{-187}+2q^{-189}-2q^{-193}+q^{-195}$
6	$q^{162}-2q^{160}-q^{158}+4q^{156}+q^{154}-2q^{152}-8q^{150}+2q^{148}+q^{146}+q^{144}+26q^{142}+16q^{140}-10q^{138}-57q^{136}-51q^{134}-36q^{132}+11q^{130}+143q^{128}+195q^{126}+137q^{124}-99q^{122}-287q^{120}-459q^{118}-410q^{116}+68q^{114}+640q^{112}+1060q^{110}+830q^{108}+173q^{106}-1009q^{104}-2023q^{102}-1941q^{100}-678q^{98}+1463q^{96}+3152q^{94}+3780q^{92}+2018q^{90}-1481q^{88}-4878q^{86}-6262q^{84}-4220q^{82}+439q^{80}+6485q^{78}+9698q^{76}+7976q^{74}+1368q^{72}-7280q^{70}-13406q^{68}-13474q^{66}-5098q^{64}+7203q^{62}+17621q^{60}+19672q^{58}+11084q^{56}-5308q^{54}-21775q^{52}-27401q^{50}-18674q^{48}+2279q^{46}+24627q^{44}+36206q^{42}+28037q^{40}+1933q^{38}-27631q^{36}-44995q^{34}-37534q^{32}-7434q^{30}+30828q^{28}+54032q^{26}+46625q^{24}+11390q^{22}-34009q^{20}-61963q^{18}-54770q^{16}-13037q^{14}+38452q^{12}+68727q^{10}+58848q^{8}+12048q^{6}-43438q^{4}-73984q^{2}-58407-6957q^{-2}+49025q^{-4}+74855q^{-6}+53464q^{-8}-1068q^{-10}-54382q^{-12}-71205q^{-14}-43129q^{-16}+11182q^{-18}+56201q^{-20}+63073q^{-22}+29354q^{-24}-21399q^{-26}-54030q^{-28}-49904q^{-30}-13807q^{-32}+27979q^{-34}+47554q^{-36}+33963q^{-38}-831q^{-40}-30454q^{-42}-36637q^{-44}-17135q^{-46}+11459q^{-48}+28743q^{-50}+23642q^{-52}+2020q^{-54}-18399q^{-56}-23685q^{-58}-10475q^{-60}+9765q^{-62}+22408q^{-64}+17744q^{-66}-709q^{-68}-19502q^{-70}-25310q^{-72}-12673q^{-74}+9875q^{-76}+28391q^{-78}+29061q^{-80}+9920q^{-82}-18642q^{-84}-38325q^{-86}-34615q^{-88}-8043q^{-90}+27888q^{-92}+49828q^{-94}+42101q^{-96}+5305q^{-98}-38941q^{-100}-62377q^{-102}-48353q^{-104}-1070q^{-106}+50855q^{-108}+74553q^{-110}+51242q^{-112}-5894q^{-114}-62108q^{-116}-81915q^{-118}-50060q^{-120}+14050q^{-122}+70810q^{-124}+82726q^{-126}+43634q^{-128}-21859q^{-130}-72909q^{-132}-77196q^{-134}-34176q^{-136}+27864q^{-138}+68391q^{-140}+65402q^{-142}+23586q^{-144}-29019q^{-146}-59027q^{-148}-50902q^{-150}-13460q^{-152}+26397q^{-154}+45962q^{-156}+36219q^{-158}+6720q^{-160}-21791q^{-162}-32919q^{-164}-23055q^{-166}-2551q^{-168}+15735q^{-170}+21601q^{-172}+13820q^{-174}+60q^{-176}-10532q^{-178}-12604q^{-180}-7602q^{-182}+590q^{-184}+6519q^{-186}+7067q^{-188}+3581q^{-190}-861q^{-192}-3460q^{-194}-3688q^{-196}-1669q^{-198}+802q^{-200}+1930q^{-202}+1655q^{-204}+571q^{-206}-408q^{-208}-1035q^{-210}-799q^{-212}-100q^{-214}+329q^{-216}+448q^{-218}+281q^{-220}+68q^{-222}-216q^{-224}-242q^{-226}-70q^{-228}+29q^{-230}+84q^{-232}+70q^{-234}+54q^{-236}-36q^{-238}-53q^{-240}-11q^{-242}+10q^{-246}+4q^{-248}+16q^{-250}-6q^{-252}-10q^{-254}+3q^{-256}+2q^{-260}-2q^{-262}+2q^{-264}-2q^{-268}+q^{-270}$

A2 Invariants.

Weight	Invariant
1,0	$q^{8}-q^{6}+2q^{4}+1+2q^{-2}-3q^{-4}+2q^{-6}-3q^{-8}+q^{-10}-q^{-14}+2q^{-16}-q^{-18}+q^{-20}$
1,1	$q^{28}-4q^{26}+12q^{24}-30q^{22}+64q^{20}-112q^{18}+188q^{16}-284q^{14}+387q^{12}-482q^{10}+544q^{8}-558q^{6}+502q^{4}-366q^{2}+172+74q^{-2}-329q^{-4}+574q^{-6}-784q^{-8}+928q^{-10}-999q^{-12}+982q^{-14}-884q^{-16}+720q^{-18}-501q^{-20}+264q^{-22}-30q^{-24}-162q^{-26}+302q^{-28}-386q^{-30}+414q^{-32}-404q^{-34}+367q^{-36}-320q^{-38}+268q^{-40}-218q^{-42}+171q^{-44}-128q^{-46}+92q^{-48}-60q^{-50}+36q^{-52}-20q^{-54}+10q^{-56}-4q^{-58}+q^{-60}$
2,0	$q^{24}-q^{22}-q^{20}+4q^{18}+2q^{16}-4q^{14}+6q^{10}-9q^{6}+7q^{2}-4-6q^{-2}+9q^{-4}+q^{-6}-5q^{-8}+4q^{-10}+5q^{-12}-3q^{-14}-4q^{-16}+9q^{-18}-9q^{-22}+3q^{-24}+8q^{-26}-7q^{-28}-5q^{-30}+6q^{-32}+q^{-34}-3q^{-36}-2q^{-38}+3q^{-40}-2q^{-44}+2q^{-46}-q^{-50}+q^{-52}$

A3 Invariants.

Weight	Invariant
0,1,0	$q^{20}-2q^{18}+q^{16}+3q^{14}-7q^{12}+5q^{10}+5q^{8}-12q^{6}+13q^{4}+7q^{2}-14+12q^{-2}+7q^{-4}-17q^{-6}+2q^{-8}+5q^{-10}-9q^{-12}-4q^{-14}+2q^{-16}+8q^{-18}-7q^{-20}-2q^{-22}+19q^{-24}-10q^{-26}-8q^{-28}+18q^{-30}-8q^{-32}-10q^{-34}+12q^{-36}-2q^{-38}-6q^{-40}+5q^{-42}-2q^{-46}+q^{-48}$
1,0,0	$q^{9}-q^{7}+3q^{5}-q^{3}+4q-q^{-1}+2q^{-3}-2q^{-5}-q^{-7}-q^{-9}-2q^{-11}+q^{-13}-2q^{-15}+3q^{-17}-2q^{-19}+3q^{-21}-q^{-23}+q^{-25}$
1,0,1	$q^{34}-4q^{32}+10q^{30}-16q^{28}+13q^{26}+10q^{24}-48q^{22}+94q^{20}-101q^{18}+51q^{16}+64q^{14}-203q^{12}+293q^{10}-283q^{8}+147q^{6}+84q^{4}-309q^{2}+458-433q^{-2}+260q^{-4}-19q^{-6}-190q^{-8}+250q^{-10}-205q^{-12}+103q^{-14}-51q^{-16}+100q^{-18}-192q^{-20}+274q^{-22}-228q^{-24}+58q^{-26}+191q^{-28}-396q^{-30}+449q^{-32}-318q^{-34}+64q^{-36}+182q^{-38}-308q^{-40}+265q^{-42}-109q^{-44}-66q^{-46}+164q^{-48}-155q^{-50}+67q^{-52}+36q^{-54}-97q^{-56}+97q^{-58}-49q^{-60}-6q^{-62}+40q^{-64}-41q^{-66}+22q^{-68}-2q^{-70}-8q^{-72}+8q^{-74}-4q^{-76}+q^{-78}$

A4 Invariants.

Weight	Invariant
0,1,0,0	$q^{22}-q^{20}+3q^{16}-3q^{14}-q^{12}+5q^{10}-2q^{8}-2q^{6}+12q^{4}+4q^{2}-5+8q^{-2}+11q^{-4}-8q^{-6}-14q^{-8}+8q^{-10}-2q^{-12}-23q^{-14}-2q^{-16}+14q^{-18}-14q^{-20}-3q^{-22}+21q^{-24}+2q^{-26}-7q^{-28}+12q^{-30}+10q^{-32}-12q^{-34}-5q^{-36}+10q^{-38}-2q^{-40}-13q^{-42}+5q^{-44}+7q^{-46}-6q^{-48}-q^{-50}+4q^{-52}-q^{-54}-q^{-56}+q^{-58}$
1,0,0,0	$q^{10}-q^{8}+3q^{6}+3q^{2}+2+2q^{-4}-3q^{-6}-4q^{-10}-3q^{-14}+q^{-16}-q^{-18}+q^{-20}+2q^{-22}-q^{-24}+3q^{-26}-q^{-28}+q^{-30}$

B2 Invariants.

Weight	Invariant
0,1	$q^{20}-2q^{18}+5q^{16}-9q^{14}+13q^{12}-17q^{10}+21q^{8}-22q^{6}+23q^{4}-17q^{2}+12-2q^{-2}-7q^{-4}+19q^{-6}-30q^{-8}+37q^{-10}-43q^{-12}+42q^{-14}-40q^{-16}+32q^{-18}-23q^{-20}+12q^{-22}-q^{-24}-8q^{-26}+16q^{-28}-20q^{-30}+22q^{-32}-20q^{-34}+18q^{-36}-14q^{-38}+10q^{-40}-7q^{-42}+4q^{-44}-2q^{-46}+q^{-48}$
1,0	$q^{34}-2q^{30}-2q^{28}+3q^{26}+6q^{24}-2q^{22}-10q^{20}-3q^{18}+13q^{16}+12q^{14}-11q^{12}-19q^{10}+3q^{8}+25q^{6}+10q^{4}-19q^{2}-18+11q^{-2}+22q^{-4}+q^{-6}-20q^{-8}-8q^{-10}+13q^{-12}+9q^{-14}-11q^{-16}-12q^{-18}+8q^{-20}+12q^{-22}-6q^{-24}-16q^{-26}+3q^{-28}+18q^{-30}+3q^{-32}-18q^{-34}-8q^{-36}+18q^{-38}+16q^{-40}-11q^{-42}-21q^{-44}+2q^{-46}+22q^{-48}+9q^{-50}-15q^{-52}-16q^{-54}+3q^{-56}+15q^{-58}+5q^{-60}-8q^{-62}-8q^{-64}+q^{-66}+6q^{-68}+2q^{-70}-2q^{-72}-2q^{-74}+q^{-78}$

D4 Invariants.

Weight

Invariant

1,0,0,0

$q^{26}-2q^{24}+3q^{22}-5q^{20}+8q^{18}-11q^{16}+12q^{14}-15q^{12}+19q^{10}-17q^{8}+19q^{6}-13q^{4}+18q^{2}-6+6q^{-2}+3q^{-4}-6q^{-6}+11q^{-8}-24q^{-10}+21q^{-12}-32q^{-14}+28q^{-16}-38q^{-18}+30q^{-20}-30q^{-22}+30q^{-24}-21q^{-26}+18q^{-28}-8q^{-30}+9q^{-32}+5q^{-34}-7q^{-36}+9q^{-38}-14q^{-40}+18q^{-42}-17q^{-44}+13q^{-46}-16q^{-48}+15q^{-50}-10q^{-52}+8q^{-54}-8q^{-56}+6q^{-58}-3q^{-60}+2q^{-62}-2q^{-64}+q^{-66}$

G2 Invariants.

Weight

Invariant

1,0

$q^{46}-2q^{44}+5q^{42}-9q^{40}+10q^{38}-9q^{36}+17q^{32}-34q^{30}+51q^{28}-55q^{26}+35q^{24}+5q^{22}-60q^{20}+111q^{18}-124q^{16}+97q^{14}-28q^{12}-55q^{10}+125q^{8}-149q^{6}+116q^{4}-36q^{2}-49+109q^{-2}-110q^{-4}+59q^{-6}+24q^{-8}-87q^{-10}+112q^{-12}-89q^{-14}+15q^{-16}+69q^{-18}-141q^{-20}+167q^{-22}-135q^{-24}+54q^{-26}+49q^{-28}-143q^{-30}+185q^{-32}-173q^{-34}+99q^{-36}-95q^{-40}+144q^{-42}-127q^{-44}+62q^{-46}+25q^{-48}-86q^{-50}+94q^{-52}-53q^{-54}-19q^{-56}+84q^{-58}-110q^{-60}+97q^{-62}-39q^{-64}-29q^{-66}+84q^{-68}-109q^{-70}+99q^{-72}-63q^{-74}+18q^{-76}+23q^{-78}-53q^{-80}+65q^{-82}-58q^{-84}+44q^{-86}-20q^{-88}-2q^{-90}+17q^{-92}-28q^{-94}+26q^{-96}-19q^{-98}+11q^{-100}-2q^{-102}-3q^{-104}+5q^{-106}-6q^{-108}+4q^{-110}-2q^{-112}+q^{-114}$

.

Computer Talk

The above data is available with the Mathematica package KnotTheory`, as shown in the (simulated) Mathematica session below. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting. This Mathematica session is also available (albeit only for the knot 5_2) as the notebook PolynomialInvariantsSession.nb.

(The path below may be different on your system, and possibly also the KnotTheory` date)

In[1]:=

AppendTo[$Path, "C:/drorbn/projects/KAtlas/"]; << KnotTheory`

Loading KnotTheory` version of August 31, 2006, 11:25:27.5625. Read more at http://katlas.math.toronto.edu/wiki/KnotTheory.

In[3]:=

K = Knot["10 94"];

In[4]:=

Alexander[K][t]

KnotTheory::loading: Loading precomputed data in PD4Knots`.

Out[4]=

$-t^{4}+4t^{3}-9t^{2}+14t-15+14t^{-1}-9t^{-2}+4t^{-3}-t^{-4}$

In[5]:=

Conway[K][z]

Out[5]=

$-z^{8}-4z^{6}-5z^{4}-2z^{2}+1$

In[6]:=

Alexander[K, 2][t]

KnotTheory::credits: The program Alexander[K, r] to compute Alexander ideals was written by Jana Archibald at the University of Toronto in the summer of 2005.

Out[6]=

$\{1\}$

In[7]:=

{KnotDet[K], KnotSignature[K]}

Out[7]=

{ 71, 2 }

In[8]:=

Jones[K][q]

KnotTheory::loading: Loading precomputed data in Jones4Knots`.

Out[8]=

$q^{7}-3q^{6}+6q^{5}-9q^{4}+11q^{3}-12q^{2}+11q-8+6q^{-1}-3q^{-2}+q^{-3}$

In[9]:=

HOMFLYPT[K][a, z]

KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.

Out[9]=

$-z^{8}a^{-2}-6z^{6}a^{-2}+z^{6}a^{-4}+z^{6}-13z^{4}a^{-2}+4z^{4}a^{-4}+4z^{4}-12z^{2}a^{-2}+5z^{2}a^{-4}+5z^{2}-4a^{-2}+2a^{-4}+3$

In[10]:=

Kauffman[K][a, z]

KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.

Out[10]=

$2z^{9}a^{-1}+2z^{9}a^{-3}+9z^{8}a^{-2}+5z^{8}a^{-4}+4z^{8}+3az^{7}+3z^{7}a^{-3}+6z^{7}a^{-5}+a^{2}z^{6}-27z^{6}a^{-2}-9z^{6}a^{-4}+5z^{6}a^{-6}-12z^{6}-9az^{5}-11z^{5}a^{-1}-15z^{5}a^{-3}-10z^{5}a^{-5}+3z^{5}a^{-7}-3a^{2}z^{4}+31z^{4}a^{-2}+10z^{4}a^{-4}-6z^{4}a^{-6}+z^{4}a^{-8}+11z^{4}+6az^{3}+10z^{3}a^{-1}+16z^{3}a^{-3}+9z^{3}a^{-5}-3z^{3}a^{-7}+2a^{2}z^{2}-18z^{2}a^{-2}-6z^{2}a^{-4}+2z^{2}a^{-6}-z^{2}a^{-8}-7z^{2}-az-3za^{-1}-5za^{-3}-3za^{-5}+4a^{-2}+2a^{-4}+3$

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {...}

Same Jones Polynomial (up to mirroring, $q\leftrightarrow q^{-1}$): {10_41, ...}

Vassiliev invariants

V2 and V3:

(-2, -2)

V2,1 through V6,9:

V2,1 V3,1 V4,1 V4,2 V4,3 V5,1 V5,2 V5,3 V5,4 V6,1 V6,2 V6,3 V6,4 V6,5 V6,6 V6,7 V6,8 V6,9 $-8$ $-16$ $32$ ${\frac {212}{3}}$ ${\frac {172}{3}}$ $128$ ${\frac {896}{3}}$ ${\frac {320}{3}}$ $80$ $-{\frac {256}{3}}$ $128$ $-{\frac {1696}{3}}$ $-{\frac {1376}{3}}$ $-{\frac {1351}{15}}$ ${\frac {9644}{15}}$ $-{\frac {48124}{45}}$ ${\frac {2167}{9}}$ $-{\frac {4951}{15}}$

V_2,1 through V_6,9 were provided by Petr Dunin-Barkowski <barkovs@itep.ru>, Andrey Smirnov <asmirnov@itep.ru>, and Alexei Sleptsov <sleptsov@itep.ru> and uploaded on October 2010 by User:Drorbn. Note that they are normalized differently than V₂ and V₃.

Khovanov Homology

The coefficients of the monomials $t^{r}q^{j}$ are shown, along with their alternating sums $\chi$ (fixed $j$, alternation over $r$). The squares with yellow highlighting are those on the "critical diagonals", where $j-2r=s+1$ or $j-2r=s-1$, where $s=$2 is the signature of 10 94. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

\   r    \    j   \ -4 -3 -2 -1 0 1 2 3 4 5 6 χ 15                     1 1 13                   2   -2 11                 4 1   3 9               5 2     -3 7             6 4       2 5           6 5         -1 3         5 6           -1 1       4 7             3 -1     2 4               -2 -3   1 4                 3 -5   2                   -2 -7 1                     1

Integral Khovanov Homology (db, data source)

$\dim {\mathcal {G}}_{2r+i}\operatorname {KH} _{\mathbb {Z} }^{r}$ $i=1$ $i=3$ $r=-4$ ${\mathbb {Z} }$ $r=-3$ ${\mathbb {Z} }^{2}\oplus {\mathbb {Z} }_{2}$ ${\mathbb {Z} }$ $r=-2$ ${\mathbb {Z} }^{4}\oplus {\mathbb {Z} }_{2}^{2}$ ${\mathbb {Z} }^{2}$ $r=-1$ ${\mathbb {Z} }^{4}\oplus {\mathbb {Z} }_{2}^{4}$ ${\mathbb {Z} }^{4}$ $r=0$ ${\mathbb {Z} }^{7}\oplus {\mathbb {Z} }_{2}^{4}$ ${\mathbb {Z} }^{5}$ $r=1$ ${\mathbb {Z} }^{6}\oplus {\mathbb {Z} }_{2}^{6}$ ${\mathbb {Z} }^{6}$ $r=2$ ${\mathbb {Z} }^{5}\oplus {\mathbb {Z} }_{2}^{6}$ ${\mathbb {Z} }^{6}$ $r=3$ ${\mathbb {Z} }^{4}\oplus {\mathbb {Z} }_{2}^{5}$ ${\mathbb {Z} }^{5}$ $r=4$ ${\mathbb {Z} }^{2}\oplus {\mathbb {Z} }_{2}^{4}$ ${\mathbb {Z} }^{4}$ $r=5$ ${\mathbb {Z} }\oplus {\mathbb {Z} }_{2}^{2}$ ${\mathbb {Z} }^{2}$ $r=6$ ${\mathbb {Z} }_{2}$ ${\mathbb {Z} }$

The Coloured Jones Polynomials

The Coloured Jones Polynomials (in the $n+1$-dimensional representation of $sl(2)$)

$n$	$J_{n}$
2	$q^{20}-3q^{19}+2q^{18}+6q^{17}-15q^{16}+9q^{15}+19q^{14}-43q^{13}+20q^{12}+46q^{11}-81q^{10}+23q^{9}+79q^{8}-104q^{7}+11q^{6}+98q^{5}-97q^{4}-9q^{3}+94q^{2}-67q-24+70q^{-1}-31q^{-2}-27q^{-3}+36q^{-4}-6q^{-5}-15q^{-6}+10q^{-7}+q^{-8}-3q^{-9}+q^{-10}$
3	$q^{39}-3q^{38}+2q^{37}+2q^{36}-7q^{34}+3q^{33}+10q^{32}-8q^{31}-14q^{30}+21q^{29}+21q^{28}-44q^{27}-43q^{26}+83q^{25}+81q^{24}-124q^{23}-146q^{22}+161q^{21}+231q^{20}-182q^{19}-321q^{18}+176q^{17}+406q^{16}-148q^{15}-469q^{14}+102q^{13}+504q^{12}-46q^{11}-509q^{10}-18q^{9}+492q^{8}+81q^{7}-456q^{6}-137q^{5}+395q^{4}+197q^{3}-332q^{2}-229q+241+259q^{-1}-161q^{-2}-245q^{-3}+71q^{-4}+219q^{-5}-9q^{-6}-164q^{-7}-37q^{-8}+112q^{-9}+46q^{-10}-58q^{-11}-44q^{-12}+26q^{-13}+29q^{-14}-8q^{-15}-15q^{-16}+2q^{-17}+5q^{-18}+q^{-19}-3q^{-20}+q^{-21}$
4	$q^{64}-3q^{63}+2q^{62}+2q^{61}-4q^{60}+8q^{59}-13q^{58}+5q^{57}+5q^{56}-13q^{55}+39q^{54}-34q^{53}-11q^{51}-49q^{50}+128q^{49}-7q^{48}+20q^{47}-112q^{46}-240q^{45}+235q^{44}+187q^{43}+271q^{42}-231q^{41}-786q^{40}+58q^{39}+473q^{38}+1020q^{37}+5q^{36}-1566q^{35}-698q^{34}+403q^{33}+2063q^{32}+874q^{31}-2018q^{30}-1745q^{29}-294q^{28}+2750q^{27}+2000q^{26}-1809q^{25}-2418q^{24}-1261q^{23}+2752q^{22}+2758q^{21}-1206q^{20}-2456q^{19}-1987q^{18}+2280q^{17}+2954q^{16}-546q^{15}-2063q^{14}-2381q^{13}+1582q^{12}+2781q^{11}+122q^{10}-1436q^{9}-2550q^{8}+703q^{7}+2313q^{6}+793q^{5}-568q^{4}-2417q^{3}-259q^{2}+1471q+1195+412q^{-1}-1778q^{-2}-906q^{-3}+396q^{-4}+996q^{-5}+1052q^{-6}-782q^{-7}-871q^{-8}-383q^{-9}+348q^{-10}+990q^{-11}-5q^{-12}-361q^{-13}-501q^{-14}-152q^{-15}+492q^{-16}+194q^{-17}+34q^{-18}-228q^{-19}-214q^{-20}+113q^{-21}+80q^{-22}+93q^{-23}-34q^{-24}-88q^{-25}+9q^{-26}+2q^{-27}+32q^{-28}+4q^{-29}-18q^{-30}+2q^{-31}-3q^{-32}+5q^{-33}+q^{-34}-3q^{-35}+q^{-36}$
5	$q^{95}-3q^{94}+2q^{93}+2q^{92}-4q^{91}+4q^{90}+2q^{89}-11q^{88}+11q^{86}+12q^{84}+4q^{83}-44q^{82}-32q^{81}+22q^{80}+61q^{79}+81q^{78}+20q^{77}-136q^{76}-211q^{75}-76q^{74}+201q^{73}+416q^{72}+296q^{71}-218q^{70}-761q^{69}-753q^{68}+68q^{67}+1191q^{66}+1559q^{65}+467q^{64}-1545q^{63}-2787q^{62}-1659q^{61}+1585q^{60}+4340q^{59}+3639q^{58}-885q^{57}-5879q^{56}-6507q^{55}-867q^{54}+7029q^{53}+9896q^{52}+3793q^{51}-7210q^{50}-13343q^{49}-7751q^{48}+6177q^{47}+16249q^{46}+12173q^{45}-3926q^{44}-18039q^{43}-16463q^{42}+767q^{41}+18567q^{40}+20004q^{39}+2694q^{38}-17892q^{37}-22400q^{36}-5971q^{35}+16382q^{34}+23618q^{33}+8658q^{32}-14466q^{31}-23833q^{30}-10608q^{29}+12469q^{28}+23334q^{27}+11921q^{26}-10514q^{25}-22459q^{24}-12816q^{23}+8650q^{22}+21309q^{21}+13516q^{20}-6687q^{19}-19936q^{18}-14173q^{17}+4472q^{16}+18273q^{15}+14765q^{14}-1980q^{13}-16079q^{12}-15114q^{11}-886q^{10}+13335q^{9}+15054q^{8}+3680q^{7}-9920q^{6}-14137q^{5}-6338q^{4}+6090q^{3}+12432q^{2}+8112q-2169-9668q^{-1}-8940q^{-2}-1349q^{-3}+6417q^{-4}+8388q^{-5}+3926q^{-6}-2899q^{-7}-6808q^{-8}-5237q^{-9}-84q^{-10}+4425q^{-11}+5228q^{-12}+2223q^{-13}-2006q^{-14}-4181q^{-15}-3107q^{-16}-73q^{-17}+2604q^{-18}+3054q^{-19}+1266q^{-20}-1079q^{-21}-2232q^{-22}-1680q^{-23}-65q^{-24}+1298q^{-25}+1450q^{-26}+592q^{-27}-467q^{-28}-957q^{-29}-678q^{-30}-13q^{-31}+478q^{-32}+511q^{-33}+186q^{-34}-169q^{-35}-277q^{-36}-174q^{-37}+130q^{-39}+113q^{-40}+19q^{-41}-41q^{-42}-39q^{-43}-29q^{-44}+6q^{-45}+27q^{-46}+6q^{-47}-6q^{-48}-q^{-49}-3q^{-50}-3q^{-51}+5q^{-52}+q^{-53}-3q^{-54}+q^{-55}$
6	$q^{132}-3q^{131}+2q^{130}+2q^{129}-4q^{128}+4q^{127}-2q^{126}+4q^{125}-16q^{124}+6q^{123}+24q^{122}-16q^{121}+10q^{120}-12q^{119}-7q^{118}-58q^{117}+23q^{116}+114q^{115}+24q^{113}-67q^{112}-106q^{111}-230q^{110}+49q^{109}+398q^{108}+213q^{107}+191q^{106}-186q^{105}-535q^{104}-929q^{103}-187q^{102}+1025q^{101}+1192q^{100}+1275q^{99}+89q^{98}-1663q^{97}-3400q^{96}-2206q^{95}+1253q^{94}+3791q^{93}+5717q^{92}+3575q^{91}-2211q^{90}-9329q^{89}-10398q^{88}-3749q^{87}+5863q^{86}+16309q^{85}+17335q^{84}+5570q^{83}-15195q^{82}-28684q^{81}-24253q^{80}-4001q^{79}+27437q^{78}+45846q^{77}+35069q^{76}-5452q^{75}-48249q^{74}-64110q^{73}-41443q^{72}+19312q^{71}+75854q^{70}+87674q^{69}+36364q^{68}-45260q^{67}-104637q^{66}-103483q^{65}-23708q^{64}+80141q^{63}+138724q^{62}+101857q^{61}-6168q^{60}-116553q^{59}-160243q^{58}-87818q^{57}+48286q^{56}+158531q^{55}+158071q^{54}+50968q^{53}-93242q^{52}-183941q^{51}-139743q^{50}+1003q^{49}+144507q^{48}+181507q^{47}+95214q^{46}-56446q^{45}-176214q^{44}-161683q^{43}-34928q^{42}+117935q^{41}+177797q^{40}+114897q^{39}-27884q^{38}-157073q^{37}-162353q^{36}-53444q^{35}+95387q^{34}+165160q^{33}+120705q^{32}-9091q^{31}-138620q^{30}-157689q^{29}-66087q^{28}+75147q^{27}+151950q^{26}+125991q^{25}+11328q^{24}-116998q^{23}-152588q^{22}-83371q^{21}+46553q^{20}+132448q^{19}+132174q^{18}+40951q^{17}-82204q^{16}-138997q^{15}-102946q^{14}+4767q^{13}+96351q^{12}+128048q^{11}+73582q^{10}-31451q^{9}-105278q^{8}-109818q^{7}-40252q^{6}+42040q^{5}+99972q^{4}+90405q^{3}+21863q^{2}-50746q-88427-66082q^{-1}-13942q^{-2}+48522q^{-3}+74828q^{-4}+52409q^{-5}+4740q^{-6}-41627q^{-7}-56203q^{-8}-44217q^{-9}-2967q^{-10}+33095q^{-11}+45216q^{-12}+32694q^{-13}+3772q^{-14}-20968q^{-15}-36810q^{-16}-26171q^{-17}-5167q^{-18}+15116q^{-19}+25233q^{-20}+21136q^{-21}+8596q^{-22}-10706q^{-23}-18002q^{-24}-16746q^{-25}-7232q^{-26}+4280q^{-27}+12409q^{-28}+14222q^{-29}+5761q^{-30}-1610q^{-31}-8158q^{-32}-9283q^{-33}-6138q^{-34}+108q^{-35}+5846q^{-36}+5829q^{-37}+4516q^{-38}+490q^{-39}-2675q^{-40}-4416q^{-41}-3105q^{-42}-200q^{-43}+1170q^{-44}+2474q^{-45}+1874q^{-46}+722q^{-47}-917q^{-48}-1343q^{-49}-828q^{-50}-519q^{-51}+333q^{-52}+611q^{-53}+640q^{-54}+97q^{-55}-161q^{-56}-171q^{-57}-289q^{-58}-87q^{-59}+39q^{-60}+162q^{-61}+48q^{-62}+11q^{-63}+17q^{-64}-53q^{-65}-29q^{-66}-13q^{-67}+30q^{-68}+q^{-69}-4q^{-70}+11q^{-71}-6q^{-72}-3q^{-73}-3q^{-74}+5q^{-75}+q^{-76}-3q^{-77}+q^{-78}$
7	$q^{175}-3q^{174}+2q^{173}+2q^{172}-4q^{171}+4q^{170}-2q^{169}-q^{167}-10q^{166}+19q^{165}+8q^{164}-18q^{163}+5q^{162}-15q^{161}-5q^{160}+q^{159}-22q^{158}+81q^{157}+52q^{156}-48q^{155}-36q^{154}-105q^{153}-34q^{152}+17q^{151}-4q^{150}+269q^{149}+221q^{148}-70q^{147}-199q^{146}-470q^{145}-260q^{144}+56q^{143}+235q^{142}+909q^{141}+813q^{140}+45q^{139}-757q^{138}-1865q^{137}-1601q^{136}-340q^{135}+1184q^{134}+3515q^{133}+3848q^{132}+1861q^{131}-1680q^{130}-6640q^{129}-8380q^{128}-5724q^{127}+802q^{126}+10672q^{125}+16707q^{124}+15085q^{123}+4513q^{122}-14385q^{121}-29965q^{120}-33273q^{119}-19039q^{118}+13087q^{117}+46263q^{116}+63451q^{115}+50372q^{114}+1733q^{113}-60331q^{112}-105985q^{111}-105078q^{110}-41237q^{109}+60425q^{108}+154271q^{107}+186189q^{106}+117900q^{105}-29815q^{104}-194866q^{103}-289047q^{102}-238228q^{101}-48084q^{100}+206381q^{99}+396985q^{98}+399254q^{97}+185801q^{96}-166238q^{95}-486164q^{94}-584376q^{93}-381608q^{92}+58293q^{91}+527985q^{90}+764882q^{89}+619520q^{88}+120754q^{87}-500862q^{86}-909006q^{85}-869481q^{84}-355415q^{83}+397541q^{82}+988808q^{81}+1095124q^{80}+617173q^{79}-227763q^{78}-991741q^{77}-1266294q^{76}-869673q^{75}+18068q^{74}+922380q^{73}+1364500q^{72}+1080639q^{71}+199484q^{70}-800665q^{69}-1389807q^{68}-1230508q^{67}-393982q^{66}+655093q^{65}+1356333q^{64}+1314536q^{63}+545256q^{62}-512090q^{61}-1286708q^{60}-1342653q^{59}-647125q^{58}+390980q^{57}+1204370q^{56}+1332481q^{55}+705063q^{54}-299606q^{53}-1126300q^{52}-1303303q^{51}-732784q^{50}+234885q^{49}+1061215q^{48}+1271349q^{47}+746410q^{46}-187597q^{45}-1009452q^{44}-1245203q^{43}-759780q^{42}+144221q^{41}+964206q^{40}+1227969q^{39}+783101q^{38}-92845q^{37}-916086q^{36}-1215920q^{35}-820069q^{34}+23538q^{33}+853711q^{32}+1201354q^{31}+869761q^{30}+69530q^{29}-767224q^{28}-1174366q^{27}-925729q^{26}-186111q^{25}+649301q^{24}+1122377q^{23}+976647q^{22}+321900q^{21}-496172q^{20}-1035467q^{19}-1008835q^{18}-464207q^{17}+311737q^{16}+904681q^{15}+1005049q^{14}+596843q^{13}-105025q^{12}-729095q^{11}-952809q^{10}-698377q^{9}-103849q^{8}+515423q^{7}+842248q^{6}+748498q^{5}+292499q^{4}-280904q^{3}-677366q^{2}-732689q-433424+51925q^{-1}+471075q^{-2}+646911q^{-3}+507064q^{-4}+142400q^{-5}-250530q^{-6}-502497q^{-7}-503040q^{-8}-275515q^{-9}+47079q^{-10}+323627q^{-11}+428409q^{-12}+332780q^{-13}+108730q^{-14}-143171q^{-15}-304628q^{-16}-315951q^{-17}-198092q^{-18}-6279q^{-19}+163929q^{-20}+242973q^{-21}+217545q^{-22}+102698q^{-23}-38052q^{-24}-143161q^{-25}-181886q^{-26}-139635q^{-27}-48441q^{-28}+47088q^{-29}+115234q^{-30}+126652q^{-31}+88156q^{-32}+23020q^{-33}-45828q^{-34}-85074q^{-35}-86621q^{-36}-57023q^{-37}-6993q^{-38}+36694q^{-39}+60738q^{-40}+60134q^{-41}+34151q^{-42}+509q^{-43}-28341q^{-44}-43758q^{-45}-38176q^{-46}-20332q^{-47}+2480q^{-48}+22238q^{-49}+28615q^{-50}+24031q^{-51}+11049q^{-52}-5012q^{-53}-14943q^{-54}-18150q^{-55}-14068q^{-56}-4414q^{-57}+4131q^{-58}+9997q^{-59}+10928q^{-60}+6630q^{-61}+1590q^{-62}-3321q^{-63}-6056q^{-64}-5363q^{-65}-3300q^{-66}-76q^{-67}+2515q^{-68}+2964q^{-69}+2534q^{-70}+1160q^{-71}-408q^{-72}-1139q^{-73}-1558q^{-74}-1057q^{-75}-148q^{-76}+288q^{-77}+613q^{-78}+543q^{-79}+272q^{-80}+100q^{-81}-217q^{-82}-303q^{-83}-136q^{-84}-58q^{-85}+53q^{-86}+66q^{-87}+42q^{-88}+79q^{-89}+2q^{-90}-44q^{-91}-24q^{-92}-14q^{-93}+11q^{-94}+4q^{-95}-9q^{-96}+13q^{-97}+6q^{-98}-6q^{-99}-3q^{-100}-3q^{-101}+5q^{-102}+q^{-103}-3q^{-104}+q^{-105}$

Computer Talk

Much of the above data can be recomputed by Mathematica using the package KnotTheory`. See A Sample KnotTheory` Session.

In[1]:=	<< KnotTheory`
Loading KnotTheory` (version of August 29, 2005, 15:27:48)...
In[2]:=	PD[Knot[10, 94]]
Out[2]=	PD[X[6, 2, 7, 1], X[2, 8, 3, 7], X[18, 12, 19, 11], X[14, 5, 15, 6], X[20, 14, 1, 13], X[8, 15, 9, 16], X[10, 4, 11, 3], X[16, 9, 17, 10], X[4, 17, 5, 18], X[12, 20, 13, 19]]
In[3]:=	GaussCode[Knot[10, 94]]
Out[3]=	GaussCode[1, -2, 7, -9, 4, -1, 2, -6, 8, -7, 3, -10, 5, -4, 6, -8, 9, -3, 10, -5]
In[4]:=	DTCode[Knot[10, 94]]
Out[4]=	DTCode[6, 10, 14, 2, 16, 18, 20, 8, 4, 12]
In[5]:=	br = BR[Knot[10, 94]]
Out[5]=	BR[3, {1, 1, 1, -2, 1, 1, -2, -2, 1, -2}]
In[6]:=	{First[br], Crossings[br]}
Out[6]=	{3, 10}
In[7]:=	BraidIndex[Knot[10, 94]]
Out[7]=	3
In[8]:=	Show[DrawMorseLink[Knot[10, 94]]]
Out[8]=	-Graphics-
In[9]:=	(#[Knot[10, 94]]&) /@ {SymmetryType, UnknottingNumber, ThreeGenus, BridgeIndex, SuperBridgeIndex, NakanishiIndex}
Out[9]=	{Chiral, 2, 4, 3, NotAvailable, 1}
In[10]:=	alex = Alexander[Knot[10, 94]][t]
Out[10]=	-4 4 9 14 2 3 4 -15 - t + -- - -- + -- + 14 t - 9 t + 4 t - t 3 2 t t t
In[11]:=	Conway[Knot[10, 94]][z]
Out[11]=	2 4 6 8 1 - 2 z - 5 z - 4 z - z
In[12]:=	Select[AllKnots[], (alex === Alexander[#][t])&]
Out[12]=	{Knot[10, 94]}
In[13]:=	{KnotDet[Knot[10, 94]], KnotSignature[Knot[10, 94]]}
Out[13]=	{71, 2}
In[14]:=	Jones[Knot[10, 94]][q]
Out[14]=	-3 3 6 2 3 4 5 6 7 -8 + q - -- + - + 11 q - 12 q + 11 q - 9 q + 6 q - 3 q + q 2 q q
In[15]:=	Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&]
Out[15]=	{Knot[10, 41], Knot[10, 94]}
In[16]:=	A2Invariant[Knot[10, 94]][q]
Out[16]=	-8 -6 2 2 4 6 8 10 14 16 1 + q - q + -- + 2 q - 3 q + 2 q - 3 q + q - q + 2 q - 4 q 18 20 q + q
In[17]:=	HOMFLYPT[Knot[10, 94]][a, z]
Out[17]=	2 2 4 4 6 2 4 2 5 z 12 z 4 4 z 13 z 6 z 3 + -- - -- + 5 z + ---- - ----- + 4 z + ---- - ----- + z + -- - 4 2 4 2 4 2 4 a a a a a a a 6 8 6 z z ---- - -- 2 2 a a
In[18]:=	Kauffman[Knot[10, 94]][a, z]
Out[18]=	2 2 2 2 2 4 3 z 5 z 3 z 2 z 2 z 6 z 18 z 3 + -- + -- - --- - --- - --- - a z - 7 z - -- + ---- - ---- - ----- + 4 2 5 3 a 8 6 4 2 a a a a a a a a 3 3 3 3 4 4 2 2 3 z 9 z 16 z 10 z 3 4 z 6 z 2 a z - ---- + ---- + ----- + ----- + 6 a z + 11 z + -- - ---- + 7 5 3 a 8 6 a a a a a 4 4 5 5 5 5 10 z 31 z 2 4 3 z 10 z 15 z 11 z 5 ----- + ----- - 3 a z + ---- - ----- - ----- - ----- - 9 a z - 4 2 7 5 3 a a a a a a 6 6 6 7 7 6 5 z 9 z 27 z 2 6 6 z 3 z 7 8 12 z + ---- - ---- - ----- + a z + ---- + ---- + 3 a z + 4 z + 6 4 2 5 3 a a a a a 8 8 9 9 5 z 9 z 2 z 2 z ---- + ---- + ---- + ---- 4 2 3 a a a a
In[19]:=	{Vassiliev[2][Knot[10, 94]], Vassiliev[3][Knot[10, 94]]}
Out[19]=	{-2, -2}
In[20]:=	Kh[Knot[10, 94]][q, t]
Out[20]=	3 1 2 1 4 2 4 4 q 7 q + 5 q + ----- + ----- + ----- + ----- + ---- + --- + --- + 7 4 5 3 3 3 3 2 2 q t t q t q t q t q t q t 3 5 5 2 7 2 7 3 9 3 9 4 6 q t + 6 q t + 5 q t + 6 q t + 4 q t + 5 q t + 2 q t + 11 4 11 5 13 5 15 6 4 q t + q t + 2 q t + q t
In[21]:=	ColouredJones[Knot[10, 94], 2][q]
Out[21]=	-10 3 -8 10 15 6 36 27 31 70 -24 + q - -- + q + -- - -- - -- + -- - -- - -- + -- - 67 q + 9 7 6 5 4 3 2 q q q q q q q q 2 3 4 5 6 7 8 9 94 q - 9 q - 97 q + 98 q + 11 q - 104 q + 79 q + 23 q - 10 11 12 13 14 15 16 17 81 q + 46 q + 20 q - 43 q + 19 q + 9 q - 15 q + 6 q + 18 19 20 2 q - 3 q + q

See/edit the Rolfsen_Splice_Template.