K13a3631
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Polynomial invariants
| Jones polynomial | Data:K13a3631/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-13 t^3+37 t^2-64 t+77-64 t^{-1} +37 t^{-2} -13 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a3631/Conway Polynomial |
| Determinant | 309 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-2} +z^8-2 a^2 z^6+4 z^6 a^{-2} -z^6 a^{-4} +2 z^6+a^4 z^4-5 a^2 z^4+8 z^4 a^{-2} -3 z^4 a^{-4} -2 z^4+2 a^4 z^2-3 a^2 z^2+10 z^2 a^{-2} -3 z^2 a^{-4} -7 z^2+a^4+6 a^{-2} -2 a^{-4} -4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{12} a^{-2} +2 z^{12}+7 a z^{11}+14 z^{11} a^{-1} +7 z^{11} a^{-3} +12 a^2 z^{10}+18 z^{10} a^{-2} +10 z^{10} a^{-4} +20 z^{10}+13 a^3 z^9+6 a z^9-22 z^9 a^{-1} -7 z^9 a^{-3} +8 z^9 a^{-5} +9 a^4 z^8-15 a^2 z^8-65 z^8 a^{-2} -28 z^8 a^{-4} +4 z^8 a^{-6} -57 z^8+4 a^5 z^7-25 a^3 z^7-37 a z^7+2 z^7 a^{-1} -15 z^7 a^{-3} -24 z^7 a^{-5} +z^7 a^{-7} +a^6 z^6-17 a^4 z^6+a^2 z^6+92 z^6 a^{-2} +31 z^6 a^{-4} -12 z^6 a^{-6} +68 z^6-7 a^5 z^5+22 a^3 z^5+45 a z^5+18 z^5 a^{-1} +28 z^5 a^{-3} +23 z^5 a^{-5} -3 z^5 a^{-7} -2 a^6 z^4+12 a^4 z^4+6 a^2 z^4-71 z^4 a^{-2} -23 z^4 a^{-4} +9 z^4 a^{-6} -47 z^4+3 a^5 z^3-14 a^3 z^3-26 a z^3-15 z^3 a^{-1} -18 z^3 a^{-3} -10 z^3 a^{-5} +2 z^3 a^{-7} +a^6 z^2-5 a^4 z^2-4 a^2 z^2+29 z^2 a^{-2} +10 z^2 a^{-4} -z^2 a^{-6} +20 z^2+4 a^3 z+7 a z+5 z a^{-1} +4 z a^{-3} +2 z a^{-5} +a^4-6 a^{-2} -2 a^{-4} -4 }[/math] |
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