K13a965
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Polynomial invariants
| Jones polynomial | Data:K13a965/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+13 t^3-37 t^2+64 t-75+64 t^{-1} -37 t^{-2} +13 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a965/Conway Polynomial |
| Determinant | 307 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -2 z^6 a^{-2} -4 z^6 a^{-4} +z^6 a^{-6} +2 z^6-a^2 z^4+2 z^4 a^{-2} -8 z^4 a^{-4} +3 z^4 a^{-6} +5 z^4-2 a^2 z^2+7 z^2 a^{-2} -9 z^2 a^{-4} +3 z^2 a^{-6} +2 z^2+5 a^{-2} -4 a^{-4} + a^{-6} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{12} a^{-2} +2 z^{12} a^{-4} +7 z^{11} a^{-1} +14 z^{11} a^{-3} +7 z^{11} a^{-5} +19 z^{10} a^{-2} +20 z^{10} a^{-4} +11 z^{10} a^{-6} +10 z^{10}+8 a z^9-4 z^9 a^{-1} -20 z^9 a^{-3} +3 z^9 a^{-5} +11 z^9 a^{-7} +4 a^2 z^8-67 z^8 a^{-2} -60 z^8 a^{-4} -14 z^8 a^{-6} +8 z^8 a^{-8} -25 z^8+a^3 z^7-23 a z^7-28 z^7 a^{-1} -11 z^7 a^{-3} -28 z^7 a^{-5} -17 z^7 a^{-7} +4 z^7 a^{-9} -12 a^2 z^6+86 z^6 a^{-2} +75 z^6 a^{-4} +5 z^6 a^{-6} -14 z^6 a^{-8} +z^6 a^{-10} +19 z^6-3 a^3 z^5+21 a z^5+46 z^5 a^{-1} +42 z^5 a^{-3} +35 z^5 a^{-5} +7 z^5 a^{-7} -8 z^5 a^{-9} +10 a^2 z^4-58 z^4 a^{-2} -52 z^4 a^{-4} -3 z^4 a^{-6} +7 z^4 a^{-8} -2 z^4 a^{-10} -8 z^4+2 a^3 z^3-10 a z^3-29 z^3 a^{-1} -31 z^3 a^{-3} -19 z^3 a^{-5} +5 z^3 a^{-9} -3 a^2 z^2+23 z^2 a^{-2} +22 z^2 a^{-4} +3 z^2 a^{-6} -z^2 a^{-8} +z^2 a^{-10} +3 z^2+2 a z+6 z a^{-1} +8 z a^{-3} +4 z a^{-5} -z a^{-7} -z a^{-9} -5 a^{-2} -4 a^{-4} - a^{-6} -1 }[/math] |
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