10 48

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Polynomial invariants

Alexander polynomial [math]\displaystyle{ t^4-3 t^3+6 t^2-9 t+11-9 t^{-1} +6 t^{-2} -3 t^{-3} + t^{-4} }[/math]
Conway polynomial [math]\displaystyle{ z^8+5 z^6+8 z^4+4 z^2+1 }[/math]
2nd Alexander ideal (db, data sources) [math]\displaystyle{ \{1\} }[/math]
Determinant and Signature { 49, 0 }
Jones polynomial [math]\displaystyle{ -q^5+2 q^4-4 q^3+6 q^2-7 q+9-7 q^{-1} +6 q^{-2} -4 q^{-3} +2 q^{-4} - q^{-5} }[/math]
HOMFLY-PT polynomial (db, data sources) [math]\displaystyle{ z^8-a^2 z^6-z^6 a^{-2} +7 z^6-5 a^2 z^4-5 z^4 a^{-2} +18 z^4-8 a^2 z^2-8 z^2 a^{-2} +20 z^2-4 a^2-4 a^{-2} +9 }[/math]
Kauffman polynomial (db, data sources) [math]\displaystyle{ a z^9+z^9 a^{-1} +2 a^2 z^8+3 z^8 a^{-2} +5 z^8+2 a^3 z^7+z^7 a^{-1} +3 z^7 a^{-3} +2 a^4 z^6-5 a^2 z^6-11 z^6 a^{-2} +2 z^6 a^{-4} -20 z^6+a^5 z^5-3 a^3 z^5-5 a z^5-11 z^5 a^{-1} -9 z^5 a^{-3} +z^5 a^{-5} -5 a^4 z^4+9 a^2 z^4+18 z^4 a^{-2} -5 z^4 a^{-4} +37 z^4-3 a^5 z^3-a^3 z^3+12 a z^3+21 z^3 a^{-1} +8 z^3 a^{-3} -3 z^3 a^{-5} +2 a^4 z^2-11 a^2 z^2-13 z^2 a^{-2} +z^2 a^{-4} -27 z^2+2 a^5 z-7 a z-9 z a^{-1} -3 z a^{-3} +z a^{-5} +4 a^2+4 a^{-2} +9 }[/math]
The A2 invariant [math]\displaystyle{ -q^{14}-2 q^{10}+4 q^2+1+4 q^{-2} -2 q^{-10} - q^{-14} }[/math]
The G2 invariant [math]\displaystyle{ q^{80}-q^{78}+3 q^{76}-4 q^{74}+3 q^{72}-q^{70}-3 q^{68}+8 q^{66}-11 q^{64}+13 q^{62}-11 q^{60}+3 q^{58}+4 q^{56}-14 q^{54}+21 q^{52}-25 q^{50}+21 q^{48}-15 q^{46}-3 q^{44}+18 q^{42}-33 q^{40}+35 q^{38}-29 q^{36}+11 q^{34}+8 q^{32}-27 q^{30}+32 q^{28}-22 q^{26}+4 q^{24}+17 q^{22}-28 q^{20}+22 q^{18}-2 q^{16}-21 q^{14}+41 q^{12}-41 q^{10}+34 q^8-4 q^6-24 q^4+51 q^2-55+51 q^{-2} -23 q^{-4} -5 q^{-6} +34 q^{-8} -41 q^{-10} +44 q^{-12} -25 q^{-14} +3 q^{-16} +19 q^{-18} -30 q^{-20} +23 q^{-22} -5 q^{-24} -17 q^{-26} +32 q^{-28} -32 q^{-30} +14 q^{-32} +7 q^{-34} -31 q^{-36} +41 q^{-38} -40 q^{-40} +21 q^{-42} - q^{-44} -20 q^{-46} +30 q^{-48} -31 q^{-50} +23 q^{-52} -10 q^{-54} -2 q^{-56} +8 q^{-58} -14 q^{-60} +12 q^{-62} -9 q^{-64} +6 q^{-66} - q^{-68} -2 q^{-70} +3 q^{-72} -3 q^{-74} +2 q^{-76} - q^{-78} + q^{-80} }[/math]
Further Quantum Invariants
Further quantum knot invariants for 10_48.

A1 Invariants.

Weight Invariant
1 [math]\displaystyle{ -q^{11}+q^9-2 q^7+2 q^5-q^3+2 q+2 q^{-1} - q^{-3} +2 q^{-5} -2 q^{-7} + q^{-9} - q^{-11} }[/math]
2 [math]\displaystyle{ q^{32}-q^{30}-q^{28}+3 q^{26}-2 q^{24}-3 q^{22}+6 q^{20}-3 q^{18}-7 q^{16}+9 q^{14}-10 q^{10}+7 q^8+4 q^6-7 q^4+2 q^2+6+2 q^{-2} -6 q^{-4} +4 q^{-6} +7 q^{-8} -10 q^{-10} + q^{-12} +9 q^{-14} -8 q^{-16} -3 q^{-18} +7 q^{-20} -3 q^{-22} -4 q^{-24} +3 q^{-26} - q^{-30} + q^{-32} }[/math]
3 [math]\displaystyle{ -q^{63}+q^{61}+q^{59}-2 q^{55}+2 q^{51}-2 q^{47}+2 q^{45}+3 q^{43}-4 q^{41}-7 q^{39}+6 q^{37}+13 q^{35}-6 q^{33}-21 q^{31}-2 q^{29}+29 q^{27}+10 q^{25}-29 q^{23}-23 q^{21}+28 q^{19}+29 q^{17}-19 q^{15}-35 q^{13}+11 q^{11}+30 q^9-26 q^5-5 q^3+19 q+16 q^{-1} -7 q^{-3} -23 q^{-5} +5 q^{-7} +28 q^{-9} +5 q^{-11} -34 q^{-13} -10 q^{-15} +35 q^{-17} +20 q^{-19} -33 q^{-21} -26 q^{-23} +22 q^{-25} +30 q^{-27} -12 q^{-29} -28 q^{-31} -2 q^{-33} +23 q^{-35} +7 q^{-37} -15 q^{-39} -11 q^{-41} +6 q^{-43} +10 q^{-45} -2 q^{-47} -5 q^{-49} + q^{-51} +3 q^{-53} - q^{-57} + q^{-61} - q^{-63} }[/math]
4 [math]\displaystyle{ q^{104}-q^{102}-q^{100}-q^{96}+4 q^{94}-q^{88}-8 q^{86}+4 q^{84}+q^{82}+7 q^{80}+8 q^{78}-13 q^{76}-6 q^{74}-14 q^{72}+10 q^{70}+32 q^{68}+5 q^{66}-6 q^{64}-50 q^{62}-24 q^{60}+40 q^{58}+51 q^{56}+46 q^{54}-62 q^{52}-94 q^{50}-24 q^{48}+61 q^{46}+140 q^{44}+15 q^{42}-116 q^{40}-130 q^{38}-19 q^{36}+174 q^{34}+126 q^{32}-41 q^{30}-168 q^{28}-120 q^{26}+108 q^{24}+156 q^{22}+47 q^{20}-109 q^{18}-140 q^{16}+19 q^{14}+103 q^{12}+77 q^{10}-33 q^8-96 q^6-31 q^4+46 q^2+75+19 q^{-2} -54 q^{-4} -81 q^{-6} +6 q^{-8} +94 q^{-10} +72 q^{-12} -32 q^{-14} -144 q^{-16} -47 q^{-18} +107 q^{-20} +141 q^{-22} +22 q^{-24} -178 q^{-26} -123 q^{-28} +57 q^{-30} +169 q^{-32} +108 q^{-34} -119 q^{-36} -153 q^{-38} -46 q^{-40} +100 q^{-42} +148 q^{-44} -4 q^{-46} -86 q^{-48} -99 q^{-50} -14 q^{-52} +91 q^{-54} +57 q^{-56} +12 q^{-58} -60 q^{-60} -60 q^{-62} +11 q^{-64} +30 q^{-66} +45 q^{-68} -2 q^{-70} -32 q^{-72} -13 q^{-74} -4 q^{-76} +22 q^{-78} +8 q^{-80} -6 q^{-82} -2 q^{-84} -7 q^{-86} +4 q^{-88} +2 q^{-90} -2 q^{-92} + q^{-94} -2 q^{-96} + q^{-98} - q^{-102} + q^{-104} }[/math]
5 [math]\displaystyle{ -q^{155}+q^{153}+q^{151}+q^{147}-q^{145}-4 q^{143}-2 q^{141}+2 q^{139}+3 q^{137}+7 q^{135}+5 q^{133}-7 q^{131}-13 q^{129}-9 q^{127}+15 q^{123}+25 q^{121}+11 q^{119}-17 q^{117}-36 q^{115}-32 q^{113}+3 q^{111}+48 q^{109}+64 q^{107}+24 q^{105}-49 q^{103}-100 q^{101}-73 q^{99}+24 q^{97}+128 q^{95}+151 q^{93}+42 q^{91}-132 q^{89}-232 q^{87}-157 q^{85}+73 q^{83}+293 q^{81}+315 q^{79}+69 q^{77}-290 q^{75}-471 q^{73}-284 q^{71}+170 q^{69}+564 q^{67}+550 q^{65}+53 q^{63}-556 q^{61}-765 q^{59}-357 q^{57}+392 q^{55}+893 q^{53}+664 q^{51}-149 q^{49}-860 q^{47}-878 q^{45}-155 q^{43}+713 q^{41}+962 q^{39}+398 q^{37}-472 q^{35}-901 q^{33}-550 q^{31}+238 q^{29}+735 q^{27}+573 q^{25}-33 q^{23}-536 q^{21}-523 q^{19}-76 q^{17}+347 q^{15}+409 q^{13}+137 q^{11}-204 q^9-329 q^7-150 q^5+123 q^3+271 q+181 q^{-1} -63 q^{-3} -264 q^{-5} -255 q^{-7} +15 q^{-9} +313 q^{-11} +355 q^{-13} +72 q^{-15} -343 q^{-17} -519 q^{-19} -203 q^{-21} +368 q^{-23} +669 q^{-25} +383 q^{-27} -300 q^{-29} -796 q^{-31} -596 q^{-33} +169 q^{-35} +829 q^{-37} +787 q^{-39} +51 q^{-41} -752 q^{-43} -910 q^{-45} -298 q^{-47} +547 q^{-49} +916 q^{-51} +524 q^{-53} -272 q^{-55} -781 q^{-57} -648 q^{-59} -42 q^{-61} +539 q^{-63} +648 q^{-65} +268 q^{-67} -243 q^{-69} -505 q^{-71} -390 q^{-73} -31 q^{-75} +301 q^{-77} +371 q^{-79} +195 q^{-81} -75 q^{-83} -258 q^{-85} -250 q^{-87} -85 q^{-89} +116 q^{-91} +207 q^{-93} +152 q^{-95} +7 q^{-97} -117 q^{-99} -146 q^{-101} -70 q^{-103} +42 q^{-105} +98 q^{-107} +77 q^{-109} +9 q^{-111} -48 q^{-113} -55 q^{-115} -27 q^{-117} +16 q^{-119} +31 q^{-121} +18 q^{-123} - q^{-125} -11 q^{-127} -13 q^{-129} -5 q^{-131} +7 q^{-133} +5 q^{-135} - q^{-141} -2 q^{-143} + q^{-145} +2 q^{-147} - q^{-149} + q^{-153} - q^{-155} }[/math]
6 [math]\displaystyle{ q^{216}-q^{214}-q^{212}-q^{208}+q^{206}+q^{204}+6 q^{202}-4 q^{198}-3 q^{196}-8 q^{194}-4 q^{192}+q^{190}+19 q^{188}+11 q^{186}+2 q^{184}-2 q^{182}-20 q^{180}-25 q^{178}-19 q^{176}+25 q^{174}+30 q^{172}+28 q^{170}+23 q^{168}-18 q^{166}-55 q^{164}-67 q^{162}+3 q^{160}+38 q^{158}+69 q^{156}+83 q^{154}+17 q^{152}-84 q^{150}-156 q^{148}-76 q^{146}+10 q^{144}+130 q^{142}+229 q^{140}+163 q^{138}-49 q^{136}-294 q^{134}-323 q^{132}-235 q^{130}+59 q^{128}+448 q^{126}+602 q^{124}+376 q^{122}-171 q^{120}-633 q^{118}-922 q^{116}-655 q^{114}+174 q^{112}+1036 q^{110}+1402 q^{108}+921 q^{106}-115 q^{104}-1445 q^{102}-2079 q^{100}-1427 q^{98}+215 q^{96}+1980 q^{94}+2741 q^{92}+2044 q^{90}-251 q^{88}-2665 q^{86}-3637 q^{84}-2439 q^{82}+419 q^{80}+3271 q^{78}+4510 q^{76}+2781 q^{74}-794 q^{72}-4072 q^{70}-4962 q^{68}-2786 q^{66}+1209 q^{64}+4754 q^{62}+5147 q^{60}+2357 q^{58}-1920 q^{56}-4923 q^{54}-4810 q^{52}-1698 q^{50}+2545 q^{48}+4784 q^{46}+3960 q^{44}+695 q^{42}-2703 q^{40}-4167 q^{38}-2905 q^{36}+178 q^{34}+2628 q^{32}+3193 q^{30}+1665 q^{28}-609 q^{26}-2218 q^{24}-2198 q^{22}-708 q^{20}+856 q^{18}+1653 q^{16}+1220 q^{14}+152 q^{12}-884 q^{10}-1173 q^8-592 q^6+280 q^4+911 q^2+819+205 q^{-2} -632 q^{-4} -1041 q^{-6} -761 q^{-8} +175 q^{-10} +1145 q^{-12} +1373 q^{-14} +696 q^{-16} -683 q^{-18} -1787 q^{-20} -1894 q^{-22} -502 q^{-24} +1497 q^{-26} +2684 q^{-28} +2193 q^{-30} +17 q^{-32} -2435 q^{-34} -3644 q^{-36} -2256 q^{-38} +828 q^{-40} +3587 q^{-42} +4179 q^{-44} +1947 q^{-46} -1702 q^{-48} -4616 q^{-50} -4393 q^{-52} -1315 q^{-54} +2668 q^{-56} +5038 q^{-58} +4195 q^{-60} +737 q^{-62} -3363 q^{-64} -5078 q^{-66} -3674 q^{-68} -102 q^{-70} +3396 q^{-72} +4701 q^{-74} +3177 q^{-76} -304 q^{-78} -3142 q^{-80} -4005 q^{-82} -2528 q^{-84} +212 q^{-86} +2603 q^{-88} +3315 q^{-90} +1973 q^{-92} -77 q^{-94} -1882 q^{-96} -2452 q^{-98} -1718 q^{-100} -144 q^{-102} +1274 q^{-104} +1701 q^{-106} +1378 q^{-108} +391 q^{-110} -617 q^{-112} -1230 q^{-114} -1091 q^{-116} -476 q^{-118} +167 q^{-120} +751 q^{-122} +870 q^{-124} +585 q^{-126} + q^{-128} -423 q^{-130} -609 q^{-132} -549 q^{-134} -151 q^{-136} +241 q^{-138} +472 q^{-140} +380 q^{-142} +175 q^{-144} -98 q^{-146} -319 q^{-148} -291 q^{-150} -128 q^{-152} +77 q^{-154} +158 q^{-156} +183 q^{-158} +99 q^{-160} -46 q^{-162} -106 q^{-164} -98 q^{-166} -31 q^{-168} +5 q^{-170} +53 q^{-172} +60 q^{-174} +13 q^{-176} -15 q^{-178} -26 q^{-180} -12 q^{-182} -12 q^{-184} +6 q^{-186} +18 q^{-188} +5 q^{-190} -2 q^{-192} -5 q^{-194} + q^{-196} -4 q^{-198} - q^{-200} +5 q^{-202} - q^{-206} -2 q^{-208} + q^{-210} - q^{-214} + q^{-216} }[/math]

A2 Invariants.

Weight Invariant
1,0 [math]\displaystyle{ -q^{14}-2 q^{10}+4 q^2+1+4 q^{-2} -2 q^{-10} - q^{-14} }[/math]
1,1 [math]\displaystyle{ q^{44}-2 q^{42}+6 q^{40}-12 q^{38}+19 q^{36}-28 q^{34}+40 q^{32}-52 q^{30}+62 q^{28}-74 q^{26}+88 q^{24}-100 q^{22}+100 q^{20}-100 q^{18}+88 q^{16}-64 q^{14}+15 q^{12}+30 q^{10}-88 q^8+142 q^6-188 q^4+228 q^2-232+246 q^{-2} -208 q^{-4} +182 q^{-6} -124 q^{-8} +72 q^{-10} -11 q^{-12} -50 q^{-14} +80 q^{-16} -116 q^{-18} +122 q^{-20} -124 q^{-22} +106 q^{-24} -88 q^{-26} +72 q^{-28} -52 q^{-30} +34 q^{-32} -24 q^{-34} +17 q^{-36} -8 q^{-38} +4 q^{-40} -2 q^{-42} + q^{-44} }[/math]
2,0 [math]\displaystyle{ q^{38}+q^{32}-q^{28}+q^{26}-3 q^{22}-3 q^{20}+q^{18}-q^{16}-7 q^{14}-q^{12}+2 q^{10}-3 q^8-2 q^6+7 q^4+6 q^2+4+7 q^{-2} +8 q^{-4} + q^{-6} - q^{-8} +4 q^{-10} - q^{-12} -6 q^{-14} -5 q^{-20} -5 q^{-22} -2 q^{-28} +2 q^{-32} + q^{-34} + q^{-38} }[/math]

A3 Invariants.

Weight Invariant
0,1,0 [math]\displaystyle{ q^{34}-q^{32}+q^{30}+2 q^{28}-3 q^{26}+q^{24}+3 q^{22}-7 q^{20}+4 q^{16}-12 q^{14}-4 q^{12}+4 q^{10}-7 q^8+10 q^4+8 q^2+8+7 q^{-2} +10 q^{-4} - q^{-6} -7 q^{-8} +3 q^{-10} -4 q^{-12} -12 q^{-14} +4 q^{-16} -7 q^{-20} +4 q^{-22} + q^{-24} -2 q^{-26} +2 q^{-28} - q^{-32} + q^{-34} }[/math]
1,0,0 [math]\displaystyle{ -q^{17}-3 q^{13}-3 q^9+q^7+4 q^3+4 q+4 q^{-1} +4 q^{-3} + q^{-7} -3 q^{-9} -3 q^{-13} - q^{-17} }[/math]
1,0,1 [math]\displaystyle{ q^{56}-2 q^{54}+5 q^{52}-5 q^{50}+2 q^{48}+5 q^{46}-15 q^{44}+20 q^{42}-16 q^{40}+2 q^{38}+16 q^{36}-31 q^{34}+33 q^{32}-10 q^{30}-19 q^{28}+53 q^{26}-58 q^{24}+34 q^{22}+15 q^{20}-86 q^{18}+94 q^{16}-109 q^{14}+20 q^{12}+19 q^{10}-84 q^8+87 q^6-40 q^4+45 q^2+30+39 q^{-2} -2 q^{-4} +65 q^{-6} -33 q^{-8} -7 q^{-10} +50 q^{-12} -121 q^{-14} +91 q^{-16} -82 q^{-18} -10 q^{-20} +50 q^{-22} -83 q^{-24} +69 q^{-26} -32 q^{-28} -2 q^{-30} +32 q^{-32} -33 q^{-34} +25 q^{-36} -8 q^{-38} -8 q^{-40} +14 q^{-42} -12 q^{-44} +7 q^{-46} + q^{-48} -3 q^{-50} +3 q^{-52} -2 q^{-54} + q^{-56} }[/math]

A4 Invariants.

Weight Invariant
0,1,0,0 [math]\displaystyle{ q^{40}+q^{36}+3 q^{34}+q^{32}+4 q^{28}-q^{26}-6 q^{24}-2 q^{22}-3 q^{20}-14 q^{18}-13 q^{16}-6 q^{14}-8 q^{12}-11 q^{10}+3 q^8+16 q^6+10 q^4+20 q^2+29+19 q^{-2} +7 q^{-4} +13 q^{-6} -13 q^{-10} -11 q^{-12} -7 q^{-14} -12 q^{-16} -13 q^{-18} -2 q^{-20} -3 q^{-24} +4 q^{-28} + q^{-32} +2 q^{-34} + q^{-40} }[/math]
1,0,0,0 [math]\displaystyle{ -q^{20}-3 q^{16}-q^{14}-3 q^{12}-2 q^{10}+5 q^4+4 q^2+7+4 q^{-2} +5 q^{-4} -2 q^{-10} -3 q^{-12} - q^{-14} -3 q^{-16} - q^{-20} }[/math]

B2 Invariants.

Weight Invariant
0,1 [math]\displaystyle{ -q^{34}+q^{32}-3 q^{30}+4 q^{28}-5 q^{26}+7 q^{24}-9 q^{22}+9 q^{20}-10 q^{18}+8 q^{16}-6 q^{14}+2 q^{12}+2 q^{10}-7 q^8+12 q^6-14 q^4+20 q^2-18+21 q^{-2} -14 q^{-4} +13 q^{-6} -7 q^{-8} +3 q^{-10} +2 q^{-12} -6 q^{-14} +8 q^{-16} -10 q^{-18} +9 q^{-20} -10 q^{-22} +7 q^{-24} -6 q^{-26} +4 q^{-28} -2 q^{-30} + q^{-32} - q^{-34} }[/math]
1,0 [math]\displaystyle{ q^{56}-q^{52}-q^{50}+2 q^{48}+3 q^{46}-q^{44}-4 q^{42}-2 q^{40}+4 q^{38}+6 q^{36}-3 q^{34}-9 q^{32}-4 q^{30}+7 q^{28}+7 q^{26}-6 q^{24}-12 q^{22}-3 q^{20}+8 q^{18}+4 q^{16}-7 q^{14}-6 q^{12}+5 q^{10}+8 q^8+q^6-4 q^4+5 q^2+10+5 q^{-2} -4 q^{-4} + q^{-6} +7 q^{-8} +5 q^{-10} -6 q^{-12} -7 q^{-14} +3 q^{-16} +8 q^{-18} -2 q^{-20} -12 q^{-22} -7 q^{-24} +7 q^{-26} +8 q^{-28} -4 q^{-30} -10 q^{-32} -3 q^{-34} +7 q^{-36} +4 q^{-38} -2 q^{-40} -4 q^{-42} +3 q^{-46} + q^{-48} - q^{-50} - q^{-52} + q^{-56} }[/math]

D4 Invariants.

Weight Invariant
1,0,0,0 [math]\displaystyle{ q^{46}-q^{44}+2 q^{42}-2 q^{40}+4 q^{38}-4 q^{36}+4 q^{34}-6 q^{32}+7 q^{30}-8 q^{28}+6 q^{26}-8 q^{24}+5 q^{22}-9 q^{20}-2 q^{18}-6 q^{16}-5 q^{14}-10 q^{10}+10 q^8-5 q^6+23 q^4-4 q^2+26-4 q^{-2} +23 q^{-4} -6 q^{-6} +10 q^{-8} -11 q^{-10} -6 q^{-14} -6 q^{-16} -3 q^{-18} -9 q^{-20} +5 q^{-22} -8 q^{-24} +7 q^{-26} -8 q^{-28} +8 q^{-30} -6 q^{-32} +5 q^{-34} -4 q^{-36} +4 q^{-38} -2 q^{-40} + q^{-42} - q^{-44} + q^{-46} }[/math]

G2 Invariants.

Weight Invariant
1,0 [math]\displaystyle{ q^{80}-q^{78}+3 q^{76}-4 q^{74}+3 q^{72}-q^{70}-3 q^{68}+8 q^{66}-11 q^{64}+13 q^{62}-11 q^{60}+3 q^{58}+4 q^{56}-14 q^{54}+21 q^{52}-25 q^{50}+21 q^{48}-15 q^{46}-3 q^{44}+18 q^{42}-33 q^{40}+35 q^{38}-29 q^{36}+11 q^{34}+8 q^{32}-27 q^{30}+32 q^{28}-22 q^{26}+4 q^{24}+17 q^{22}-28 q^{20}+22 q^{18}-2 q^{16}-21 q^{14}+41 q^{12}-41 q^{10}+34 q^8-4 q^6-24 q^4+51 q^2-55+51 q^{-2} -23 q^{-4} -5 q^{-6} +34 q^{-8} -41 q^{-10} +44 q^{-12} -25 q^{-14} +3 q^{-16} +19 q^{-18} -30 q^{-20} +23 q^{-22} -5 q^{-24} -17 q^{-26} +32 q^{-28} -32 q^{-30} +14 q^{-32} +7 q^{-34} -31 q^{-36} +41 q^{-38} -40 q^{-40} +21 q^{-42} - q^{-44} -20 q^{-46} +30 q^{-48} -31 q^{-50} +23 q^{-52} -10 q^{-54} -2 q^{-56} +8 q^{-58} -14 q^{-60} +12 q^{-62} -9 q^{-64} +6 q^{-66} - q^{-68} -2 q^{-70} +3 q^{-72} -3 q^{-74} +2 q^{-76} - q^{-78} + q^{-80} }[/math]

.

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 48"];
In[4]:= Alexander[K][t]
KnotTheory::loading: Loading precomputed data in PD4Knots`.
Out[4]= [math]\displaystyle{ t^4-3 t^3+6 t^2-9 t+11-9 t^{-1} +6 t^{-2} -3 t^{-3} + t^{-4} }[/math]
In[5]:= Conway[K][z]
Out[5]= [math]\displaystyle{ z^8+5 z^6+8 z^4+4 z^2+1 }[/math]
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]= [math]\displaystyle{ \{1\} }[/math]
In[7]:= {KnotDet[K], KnotSignature[K]}
Out[7]= { 49, 0 }
In[8]:= Jones[K][q]
KnotTheory::loading: Loading precomputed data in Jones4Knots`.
Out[8]= [math]\displaystyle{ -q^5+2 q^4-4 q^3+6 q^2-7 q+9-7 q^{-1} +6 q^{-2} -4 q^{-3} +2 q^{-4} - q^{-5} }[/math]
In[9]:= HOMFLYPT[K][a, z]
KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.
Out[9]= [math]\displaystyle{ z^8-a^2 z^6-z^6 a^{-2} +7 z^6-5 a^2 z^4-5 z^4 a^{-2} +18 z^4-8 a^2 z^2-8 z^2 a^{-2} +20 z^2-4 a^2-4 a^{-2} +9 }[/math]
In[10]:= Kauffman[K][a, z]
KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.
Out[10]= [math]\displaystyle{ a z^9+z^9 a^{-1} +2 a^2 z^8+3 z^8 a^{-2} +5 z^8+2 a^3 z^7+z^7 a^{-1} +3 z^7 a^{-3} +2 a^4 z^6-5 a^2 z^6-11 z^6 a^{-2} +2 z^6 a^{-4} -20 z^6+a^5 z^5-3 a^3 z^5-5 a z^5-11 z^5 a^{-1} -9 z^5 a^{-3} +z^5 a^{-5} -5 a^4 z^4+9 a^2 z^4+18 z^4 a^{-2} -5 z^4 a^{-4} +37 z^4-3 a^5 z^3-a^3 z^3+12 a z^3+21 z^3 a^{-1} +8 z^3 a^{-3} -3 z^3 a^{-5} +2 a^4 z^2-11 a^2 z^2-13 z^2 a^{-2} +z^2 a^{-4} -27 z^2+2 a^5 z-7 a z-9 z a^{-1} -3 z a^{-3} +z a^{-5} +4 a^2+4 a^{-2} +9 }[/math]
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