10 64

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Polynomial invariants

Alexander polynomial [math]\displaystyle{ -t^4+3 t^3-6 t^2+10 t-11+10 t^{-1} -6 t^{-2} +3 t^{-3} - t^{-4} }[/math]
Conway polynomial [math]\displaystyle{ -z^8-5 z^6-8 z^4-3 z^2+1 }[/math]
2nd Alexander ideal (db, data sources) [math]\displaystyle{ \{1\} }[/math]
Determinant and Signature { 51, 2 }
Jones polynomial [math]\displaystyle{ q^7-2 q^6+4 q^5-7 q^4+8 q^3-8 q^2+8 q-6+4 q^{-1} -2 q^{-2} + q^{-3} }[/math]
HOMFLY-PT polynomial (db, data sources) [math]\displaystyle{ -z^8 a^{-2} -7 z^6 a^{-2} +z^6 a^{-4} +z^6-18 z^4 a^{-2} +5 z^4 a^{-4} +5 z^4-19 z^2 a^{-2} +8 z^2 a^{-4} +8 z^2-6 a^{-2} +3 a^{-4} +4 }[/math]
Kauffman polynomial (db, data sources) [math]\displaystyle{ z^9 a^{-1} +z^9 a^{-3} +5 z^8 a^{-2} +3 z^8 a^{-4} +2 z^8+2 a z^7+2 z^7 a^{-3} +4 z^7 a^{-5} +a^2 z^6-18 z^6 a^{-2} -8 z^6 a^{-4} +3 z^6 a^{-6} -6 z^6-7 a z^5-5 z^5 a^{-1} -11 z^5 a^{-3} -11 z^5 a^{-5} +2 z^5 a^{-7} -4 a^2 z^4+30 z^4 a^{-2} +13 z^4 a^{-4} -5 z^4 a^{-6} +z^4 a^{-8} +7 z^4+6 a z^3+4 z^3 a^{-1} +16 z^3 a^{-3} +15 z^3 a^{-5} -3 z^3 a^{-7} +4 a^2 z^2-26 z^2 a^{-2} -8 z^2 a^{-4} +3 z^2 a^{-6} -2 z^2 a^{-8} -9 z^2-a z-3 z a^{-1} -6 z a^{-3} -4 z a^{-5} +6 a^{-2} +3 a^{-4} +4 }[/math]
The A2 invariant [math]\displaystyle{ q^8+2 q^4+ q^{-2} -2 q^{-4} +2 q^{-6} -2 q^{-8} - q^{-12} - q^{-14} +2 q^{-16} + q^{-20} }[/math]
The G2 invariant [math]\displaystyle{ q^{46}-q^{44}+3 q^{42}-5 q^{40}+4 q^{38}-3 q^{36}-2 q^{34}+9 q^{32}-14 q^{30}+20 q^{28}-18 q^{26}+9 q^{24}+5 q^{22}-22 q^{20}+37 q^{18}-41 q^{16}+33 q^{14}-10 q^{12}-16 q^{10}+43 q^8-48 q^6+42 q^4-16 q^2-11+32 q^{-2} -38 q^{-4} +24 q^{-6} +4 q^{-8} -26 q^{-10} +42 q^{-12} -30 q^{-14} +4 q^{-16} +21 q^{-18} -49 q^{-20} +58 q^{-22} -52 q^{-24} +18 q^{-26} +13 q^{-28} -48 q^{-30} +68 q^{-32} -63 q^{-34} +33 q^{-36} -5 q^{-38} -28 q^{-40} +46 q^{-42} -49 q^{-44} +26 q^{-46} +3 q^{-48} -21 q^{-50} +34 q^{-52} -22 q^{-54} -3 q^{-56} +28 q^{-58} -36 q^{-60} +34 q^{-62} -18 q^{-64} -5 q^{-66} +29 q^{-68} -39 q^{-70} +43 q^{-72} -27 q^{-74} +9 q^{-76} +8 q^{-78} -21 q^{-80} +23 q^{-82} -23 q^{-84} +18 q^{-86} -8 q^{-88} - q^{-90} +7 q^{-92} -10 q^{-94} +9 q^{-96} -7 q^{-98} +5 q^{-100} -2 q^{-102} - q^{-104} +2 q^{-106} -3 q^{-108} +2 q^{-110} - q^{-112} + q^{-114} }[/math]
Further Quantum Invariants
Further quantum knot invariants for 10_64.

A1 Invariants.

Weight Invariant
1 [math]\displaystyle{ q^7-q^5+2 q^3-2 q+2 q^{-1} + q^{-7} -3 q^{-9} +2 q^{-11} - q^{-13} + q^{-15} }[/math]
2 [math]\displaystyle{ q^{22}-q^{20}-q^{18}+4 q^{16}-q^{14}-5 q^{12}+7 q^{10}+q^8-11 q^6+6 q^4+6 q^2-11+2 q^{-2} +10 q^{-4} -5 q^{-6} -3 q^{-8} +7 q^{-10} +2 q^{-12} -6 q^{-14} -2 q^{-16} +9 q^{-18} -7 q^{-20} -7 q^{-22} +13 q^{-24} -3 q^{-26} -7 q^{-28} +7 q^{-30} -4 q^{-34} +2 q^{-36} - q^{-40} + q^{-42} }[/math]
3 [math]\displaystyle{ q^{45}-q^{43}-q^{41}+q^{39}+3 q^{37}-q^{35}-5 q^{33}+9 q^{29}+2 q^{27}-13 q^{25}-9 q^{23}+16 q^{21}+18 q^{19}-14 q^{17}-29 q^{15}+6 q^{13}+37 q^{11}+6 q^9-37 q^7-20 q^5+33 q^3+33 q-25 q^{-1} -39 q^{-3} +15 q^{-5} +43 q^{-7} -3 q^{-9} -41 q^{-11} -3 q^{-13} +38 q^{-15} +11 q^{-17} -29 q^{-19} -19 q^{-21} +16 q^{-23} +26 q^{-25} -7 q^{-27} -33 q^{-29} -11 q^{-31} +37 q^{-33} +22 q^{-35} -33 q^{-37} -33 q^{-39} +30 q^{-41} +40 q^{-43} -19 q^{-45} -34 q^{-47} +5 q^{-49} +29 q^{-51} -18 q^{-55} -5 q^{-57} +9 q^{-59} +4 q^{-61} -4 q^{-63} -2 q^{-65} +2 q^{-67} + q^{-69} - q^{-71} - q^{-79} + q^{-81} }[/math]
4 [math]\displaystyle{ q^{76}-q^{74}-q^{72}+q^{70}+3 q^{66}-3 q^{64}-3 q^{62}+3 q^{60}+9 q^{56}-6 q^{54}-13 q^{52}-q^{50}+4 q^{48}+31 q^{46}+3 q^{44}-29 q^{42}-32 q^{40}-20 q^{38}+60 q^{36}+57 q^{34}+q^{32}-66 q^{30}-103 q^{28}+23 q^{26}+103 q^{24}+105 q^{22}-7 q^{20}-166 q^{18}-102 q^{16}+32 q^{14}+175 q^{12}+141 q^{10}-96 q^8-186 q^6-121 q^4+117 q^2+233+46 q^{-2} -150 q^{-4} -214 q^{-6} +2 q^{-8} +212 q^{-10} +137 q^{-12} -70 q^{-14} -205 q^{-16} -58 q^{-18} +144 q^{-20} +143 q^{-22} -19 q^{-24} -154 q^{-26} -79 q^{-28} +76 q^{-30} +134 q^{-32} +26 q^{-34} -102 q^{-36} -114 q^{-38} -8 q^{-40} +128 q^{-42} +109 q^{-44} -12 q^{-46} -157 q^{-48} -140 q^{-50} +80 q^{-52} +191 q^{-54} +129 q^{-56} -127 q^{-58} -252 q^{-60} -39 q^{-62} +168 q^{-64} +231 q^{-66} -9 q^{-68} -227 q^{-70} -133 q^{-72} +38 q^{-74} +192 q^{-76} +90 q^{-78} -91 q^{-80} -108 q^{-82} -54 q^{-84} +73 q^{-86} +76 q^{-88} +4 q^{-90} -25 q^{-92} -50 q^{-94} +2 q^{-96} +22 q^{-98} +12 q^{-100} +8 q^{-102} -19 q^{-104} -3 q^{-106} +2 q^{-108} + q^{-110} +7 q^{-112} -6 q^{-114} + q^{-118} - q^{-120} +3 q^{-122} -2 q^{-124} - q^{-130} + q^{-132} }[/math]
5 [math]\displaystyle{ q^{115}-q^{113}-q^{111}+q^{109}+q^{103}-q^{101}-2 q^{99}+3 q^{97}+4 q^{95}-2 q^{93}-3 q^{91}-6 q^{89}-7 q^{87}+4 q^{85}+18 q^{83}+17 q^{81}+2 q^{79}-22 q^{77}-41 q^{75}-29 q^{73}+17 q^{71}+66 q^{69}+76 q^{67}+21 q^{65}-71 q^{63}-134 q^{61}-106 q^{59}+25 q^{57}+178 q^{55}+222 q^{53}+89 q^{51}-146 q^{49}-322 q^{47}-278 q^{45}+10 q^{43}+349 q^{41}+467 q^{39}+237 q^{37}-224 q^{35}-581 q^{33}-539 q^{31}-56 q^{29}+540 q^{27}+782 q^{25}+440 q^{23}-293 q^{21}-881 q^{19}-831 q^{17}-103 q^{15}+775 q^{13}+1098 q^{11}+560 q^9-473 q^7-1188 q^5-962 q^3+74 q+1082 q^{-1} +1208 q^{-3} +334 q^{-5} -834 q^{-7} -1285 q^{-9} -641 q^{-11} +539 q^{-13} +1207 q^{-15} +801 q^{-17} -258 q^{-19} -1024 q^{-21} -836 q^{-23} +74 q^{-25} +821 q^{-27} +764 q^{-29} +29 q^{-31} -642 q^{-33} -652 q^{-35} -69 q^{-37} +519 q^{-39} +561 q^{-41} +75 q^{-43} -444 q^{-45} -521 q^{-47} -121 q^{-49} +382 q^{-51} +540 q^{-53} +235 q^{-55} -289 q^{-57} -610 q^{-59} -438 q^{-61} +130 q^{-63} +650 q^{-65} +706 q^{-67} +157 q^{-69} -629 q^{-71} -983 q^{-73} -511 q^{-75} +469 q^{-77} +1167 q^{-79} +931 q^{-81} -167 q^{-83} -1211 q^{-85} -1259 q^{-87} -229 q^{-89} +1034 q^{-91} +1442 q^{-93} +631 q^{-95} -697 q^{-97} -1415 q^{-99} -919 q^{-101} +278 q^{-103} +1148 q^{-105} +1039 q^{-107} +119 q^{-109} -785 q^{-111} -943 q^{-113} -361 q^{-115} +379 q^{-117} +711 q^{-119} +456 q^{-121} -75 q^{-123} -430 q^{-125} -400 q^{-127} -102 q^{-129} +187 q^{-131} +274 q^{-133} +155 q^{-135} -33 q^{-137} -148 q^{-139} -134 q^{-141} -31 q^{-143} +58 q^{-145} +82 q^{-147} +46 q^{-149} -11 q^{-151} -42 q^{-153} -34 q^{-155} -2 q^{-157} +18 q^{-159} +16 q^{-161} +5 q^{-163} -4 q^{-165} -11 q^{-167} -3 q^{-169} +6 q^{-171} + q^{-173} - q^{-175} + q^{-177} -2 q^{-179} - q^{-181} +3 q^{-183} + q^{-185} -2 q^{-187} - q^{-193} + q^{-195} }[/math]
6 [math]\displaystyle{ q^{162}-q^{160}-q^{158}+q^{156}-2 q^{150}+3 q^{148}-2 q^{144}+5 q^{142}+2 q^{140}-2 q^{138}-12 q^{136}-q^{134}-2 q^{132}-2 q^{130}+18 q^{128}+21 q^{126}+13 q^{124}-22 q^{122}-20 q^{120}-36 q^{118}-39 q^{116}+13 q^{114}+61 q^{112}+90 q^{110}+40 q^{108}+10 q^{106}-85 q^{104}-168 q^{102}-136 q^{100}-16 q^{98}+156 q^{96}+230 q^{94}+283 q^{92}+105 q^{90}-197 q^{88}-435 q^{86}-465 q^{84}-213 q^{82}+153 q^{80}+662 q^{78}+796 q^{76}+484 q^{74}-180 q^{72}-855 q^{70}-1166 q^{68}-956 q^{66}+49 q^{64}+1097 q^{62}+1710 q^{60}+1413 q^{58}+301 q^{56}-1199 q^{54}-2367 q^{52}-2123 q^{50}-747 q^{48}+1304 q^{46}+2843 q^{44}+3052 q^{42}+1454 q^{40}-1330 q^{38}-3457 q^{36}-3970 q^{34}-2171 q^{32}+1038 q^{30}+4145 q^{28}+5036 q^{26}+2908 q^{24}-936 q^{22}-4704 q^{20}-5934 q^{18}-3789 q^{16}+1007 q^{14}+5409 q^{12}+6709 q^{10}+4177 q^8-1149 q^6-5988 q^4-7443 q^2-4118+1718 q^{-2} +6545 q^{-4} +7487 q^{-6} +3689 q^{-8} -2416 q^{-10} -7082 q^{-12} -6985 q^{-14} -2608 q^{-16} +3284 q^{-18} +6952 q^{-20} +6005 q^{-22} +1267 q^{-24} -4129 q^{-26} -6309 q^{-28} -4384 q^{-30} +240 q^{-32} +4315 q^{-34} +5192 q^{-36} +2570 q^{-38} -1545 q^{-40} -3988 q^{-42} -3573 q^{-44} -753 q^{-46} +2156 q^{-48} +3214 q^{-50} +1870 q^{-52} -679 q^{-54} -2296 q^{-56} -2125 q^{-58} -319 q^{-60} +1503 q^{-62} +2130 q^{-64} +1094 q^{-66} -793 q^{-68} -2071 q^{-70} -1920 q^{-72} -298 q^{-74} +1552 q^{-76} +2589 q^{-78} +1922 q^{-80} -92 q^{-82} -2336 q^{-84} -3328 q^{-86} -2201 q^{-88} +394 q^{-90} +3259 q^{-92} +4354 q^{-94} +2810 q^{-96} -938 q^{-98} -4531 q^{-100} -5553 q^{-102} -3206 q^{-104} +1687 q^{-106} +5972 q^{-108} +6856 q^{-110} +3130 q^{-112} -2840 q^{-114} -7325 q^{-116} -7515 q^{-118} -2727 q^{-120} +3991 q^{-122} +8464 q^{-124} +7393 q^{-126} +1768 q^{-128} -4898 q^{-130} -8594 q^{-132} -6745 q^{-134} -793 q^{-136} +5505 q^{-138} +7863 q^{-140} +5436 q^{-142} -17 q^{-144} -5161 q^{-146} -6676 q^{-148} -4087 q^{-150} +690 q^{-152} +4276 q^{-154} +5025 q^{-156} +2857 q^{-158} -717 q^{-160} -3277 q^{-162} -3556 q^{-164} -1749 q^{-166} +523 q^{-168} +2151 q^{-170} +2339 q^{-172} +1156 q^{-174} -367 q^{-176} -1342 q^{-178} -1342 q^{-180} -762 q^{-182} +130 q^{-184} +785 q^{-186} +817 q^{-188} +432 q^{-190} -55 q^{-192} -360 q^{-194} -483 q^{-196} -291 q^{-198} +33 q^{-200} +213 q^{-202} +236 q^{-204} +147 q^{-206} +26 q^{-208} -129 q^{-210} -147 q^{-212} -57 q^{-214} +8 q^{-216} +51 q^{-218} +61 q^{-220} +49 q^{-222} -18 q^{-224} -42 q^{-226} -17 q^{-228} -7 q^{-230} +4 q^{-232} +10 q^{-234} +19 q^{-236} -3 q^{-238} -11 q^{-240} + q^{-242} - q^{-244} -2 q^{-248} +5 q^{-250} - q^{-252} -4 q^{-254} +3 q^{-256} + q^{-258} + q^{-260} -2 q^{-262} - q^{-268} + q^{-270} }[/math]

A2 Invariants.

Weight Invariant
1,0 [math]\displaystyle{ q^8+2 q^4+ q^{-2} -2 q^{-4} +2 q^{-6} -2 q^{-8} - q^{-12} - q^{-14} +2 q^{-16} + q^{-20} }[/math]
1,1 [math]\displaystyle{ q^{28}-2 q^{26}+6 q^{24}-14 q^{22}+25 q^{20}-36 q^{18}+62 q^{16}-84 q^{14}+106 q^{12}-130 q^{10}+148 q^8-154 q^6+130 q^4-100 q^2+58+16 q^{-2} -90 q^{-4} +158 q^{-6} -214 q^{-8} +258 q^{-10} -288 q^{-12} +282 q^{-14} -256 q^{-16} +216 q^{-18} -152 q^{-20} +92 q^{-22} -22 q^{-24} -32 q^{-26} +85 q^{-28} -116 q^{-30} +116 q^{-32} -124 q^{-34} +117 q^{-36} -102 q^{-38} +76 q^{-40} -60 q^{-42} +54 q^{-44} -36 q^{-46} +24 q^{-48} -18 q^{-50} +13 q^{-52} -8 q^{-54} +4 q^{-56} -2 q^{-58} + q^{-60} }[/math]
2,0 [math]\displaystyle{ q^{24}+2 q^{18}+2 q^{16}-q^{14}+q^{12}+3 q^{10}-5 q^6-2 q^4+q^2-6-5 q^{-2} +4 q^{-4} +2 q^{-6} +5 q^{-10} +7 q^{-12} + q^{-14} +4 q^{-18} - q^{-20} -7 q^{-22} - q^{-24} +3 q^{-26} -4 q^{-28} +4 q^{-32} + q^{-34} -3 q^{-36} -2 q^{-38} + q^{-40} - q^{-42} - q^{-44} + q^{-46} + q^{-48} + q^{-52} }[/math]

A3 Invariants.

Weight Invariant
0,1,0 [math]\displaystyle{ q^{20}-q^{18}+q^{16}+q^{14}-4 q^{12}+2 q^{10}+3 q^8-4 q^6+8 q^4+6 q^2-6+7 q^{-2} +3 q^{-4} -11 q^{-6} - q^{-8} -6 q^{-12} -4 q^{-14} + q^{-16} +4 q^{-18} -2 q^{-20} + q^{-22} +11 q^{-24} -3 q^{-26} -4 q^{-28} +10 q^{-30} -5 q^{-32} -6 q^{-34} +6 q^{-36} - q^{-38} -3 q^{-40} +2 q^{-42} - q^{-46} + q^{-48} }[/math]
1,0,0 [math]\displaystyle{ q^9+3 q^5+3 q- q^{-1} + q^{-3} -2 q^{-5} - q^{-7} - q^{-9} -2 q^{-11} -2 q^{-15} +2 q^{-17} - q^{-19} +3 q^{-21} + q^{-25} }[/math]
1,0,1 [math]\displaystyle{ q^{34}-2 q^{32}+5 q^{30}-7 q^{28}+4 q^{26}+3 q^{24}-12 q^{22}+31 q^{20}-23 q^{18}+16 q^{16}+14 q^{14}-53 q^{12}+72 q^{10}-72 q^8+33 q^6+28 q^4-85 q^2+125-105 q^{-2} +59 q^{-4} -3 q^{-6} -67 q^{-8} +69 q^{-10} -72 q^{-12} +34 q^{-14} -8 q^{-16} +22 q^{-18} -30 q^{-20} +77 q^{-22} -47 q^{-24} +12 q^{-26} +63 q^{-28} -114 q^{-30} +112 q^{-32} -82 q^{-34} +8 q^{-36} +51 q^{-38} -93 q^{-40} +80 q^{-42} -36 q^{-44} -19 q^{-46} +52 q^{-48} -51 q^{-50} +18 q^{-52} +11 q^{-54} -21 q^{-56} +26 q^{-58} -10 q^{-60} -2 q^{-62} +8 q^{-64} -10 q^{-66} +7 q^{-68} - q^{-70} -3 q^{-72} +3 q^{-74} -2 q^{-76} + q^{-78} }[/math]

A4 Invariants.

Weight Invariant
0,1,0,0 [math]\displaystyle{ q^{22}+q^{18}+2 q^{16}-q^{14}-q^{12}+2 q^{10}-q^8-q^6+8 q^4+5 q^2+2+7 q^{-2} +8 q^{-4} -4 q^{-6} -11 q^{-8} -2 q^{-10} -8 q^{-12} -17 q^{-14} -7 q^{-16} +6 q^{-18} -6 q^{-20} +2 q^{-22} +15 q^{-24} +6 q^{-26} + q^{-28} +8 q^{-30} +7 q^{-32} -6 q^{-34} -3 q^{-36} +3 q^{-38} -2 q^{-40} -8 q^{-42} + q^{-44} +3 q^{-46} -3 q^{-48} +2 q^{-52} + q^{-58} }[/math]
1,0,0,0 [math]\displaystyle{ q^{10}+3 q^6+q^4+3 q^2+2+ q^{-4} -3 q^{-6} - q^{-8} -4 q^{-10} - q^{-12} -3 q^{-14} - q^{-18} + q^{-20} +2 q^{-22} +3 q^{-26} + q^{-30} }[/math]

B2 Invariants.

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

D4 Invariants.

Weight Invariant
1,0,0,0 [math]\displaystyle{ q^{26}-q^{24}+2 q^{22}-3 q^{20}+4 q^{18}-6 q^{16}+5 q^{14}-7 q^{12}+10 q^{10}-7 q^8+11 q^6-4 q^4+12 q^2+5 q^{-2} +2 q^{-4} -3 q^{-6} +3 q^{-8} -15 q^{-10} +7 q^{-12} -20 q^{-14} +10 q^{-16} -22 q^{-18} +13 q^{-20} -15 q^{-22} +16 q^{-24} -9 q^{-26} +12 q^{-28} -2 q^{-30} +8 q^{-32} +4 q^{-34} -2 q^{-36} +4 q^{-38} -7 q^{-40} +9 q^{-42} -9 q^{-44} +6 q^{-46} -9 q^{-48} +8 q^{-50} -5 q^{-52} +4 q^{-54} -4 q^{-56} +3 q^{-58} -2 q^{-60} + q^{-62} - q^{-64} + q^{-66} }[/math]

G2 Invariants.

Weight Invariant
1,0 [math]\displaystyle{ q^{46}-q^{44}+3 q^{42}-5 q^{40}+4 q^{38}-3 q^{36}-2 q^{34}+9 q^{32}-14 q^{30}+20 q^{28}-18 q^{26}+9 q^{24}+5 q^{22}-22 q^{20}+37 q^{18}-41 q^{16}+33 q^{14}-10 q^{12}-16 q^{10}+43 q^8-48 q^6+42 q^4-16 q^2-11+32 q^{-2} -38 q^{-4} +24 q^{-6} +4 q^{-8} -26 q^{-10} +42 q^{-12} -30 q^{-14} +4 q^{-16} +21 q^{-18} -49 q^{-20} +58 q^{-22} -52 q^{-24} +18 q^{-26} +13 q^{-28} -48 q^{-30} +68 q^{-32} -63 q^{-34} +33 q^{-36} -5 q^{-38} -28 q^{-40} +46 q^{-42} -49 q^{-44} +26 q^{-46} +3 q^{-48} -21 q^{-50} +34 q^{-52} -22 q^{-54} -3 q^{-56} +28 q^{-58} -36 q^{-60} +34 q^{-62} -18 q^{-64} -5 q^{-66} +29 q^{-68} -39 q^{-70} +43 q^{-72} -27 q^{-74} +9 q^{-76} +8 q^{-78} -21 q^{-80} +23 q^{-82} -23 q^{-84} +18 q^{-86} -8 q^{-88} - q^{-90} +7 q^{-92} -10 q^{-94} +9 q^{-96} -7 q^{-98} +5 q^{-100} -2 q^{-102} - q^{-104} +2 q^{-106} -3 q^{-108} +2 q^{-110} - q^{-112} + q^{-114} }[/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 64"];
In[4]:= Alexander[K][t]
KnotTheory::loading: Loading precomputed data in PD4Knots`.
Out[4]= [math]\displaystyle{ -t^4+3 t^3-6 t^2+10 t-11+10 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^4-3 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]= { 51, 2 }
In[8]:= Jones[K][q]
KnotTheory::loading: Loading precomputed data in Jones4Knots`.
Out[8]= [math]\displaystyle{ q^7-2 q^6+4 q^5-7 q^4+8 q^3-8 q^2+8 q-6+4 q^{-1} -2 q^{-2} + q^{-3} }[/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} -7 z^6 a^{-2} +z^6 a^{-4} +z^6-18 z^4 a^{-2} +5 z^4 a^{-4} +5 z^4-19 z^2 a^{-2} +8 z^2 a^{-4} +8 z^2-6 a^{-2} +3 a^{-4} +4 }[/math]
In[10]:= Kauffman[K][a, z]
KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.
Out[10]= [math]\displaystyle{ z^9 a^{-1} +z^9 a^{-3} +5 z^8 a^{-2} +3 z^8 a^{-4} +2 z^8+2 a z^7+2 z^7 a^{-3} +4 z^7 a^{-5} +a^2 z^6-18 z^6 a^{-2} -8 z^6 a^{-4} +3 z^6 a^{-6} -6 z^6-7 a z^5-5 z^5 a^{-1} -11 z^5 a^{-3} -11 z^5 a^{-5} +2 z^5 a^{-7} -4 a^2 z^4+30 z^4 a^{-2} +13 z^4 a^{-4} -5 z^4 a^{-6} +z^4 a^{-8} +7 z^4+6 a z^3+4 z^3 a^{-1} +16 z^3 a^{-3} +15 z^3 a^{-5} -3 z^3 a^{-7} +4 a^2 z^2-26 z^2 a^{-2} -8 z^2 a^{-4} +3 z^2 a^{-6} -2 z^2 a^{-8} -9 z^2-a z-3 z a^{-1} -6 z a^{-3} -4 z a^{-5} +6 a^{-2} +3 a^{-4} +4 }[/math]
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