K12a54
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+4 q^6-9 q^5+15 q^4-21 q^3+25 q^2-26 q+25-19 q^{-1} +13 q^{-2} -7 q^{-3} +3 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+17 t^2-39 t+51-39 t^{-1} +17 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^6-z^4+2 z^2+1 }[/math] |
| Determinant | 169 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -2 z^6 a^{-2} -z^6+2 a^2 z^4-6 z^4 a^{-2} +3 z^4 a^{-4} -a^4 z^2+3 a^2 z^2-8 z^2 a^{-2} +6 z^2 a^{-4} -z^2 a^{-6} +3 z^2-a^4+a^2-4 a^{-2} +3 a^{-4} - a^{-6} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +8 z^{10} a^{-2} +4 z^{10} a^{-4} +4 z^{10}+6 a z^9+14 z^9 a^{-1} +14 z^9 a^{-3} +6 z^9 a^{-5} +6 a^2 z^8-5 z^8 a^{-2} +z^8 a^{-4} +4 z^8 a^{-6} +4 z^8+5 a^3 z^7-3 a z^7-37 z^7 a^{-1} -46 z^7 a^{-3} -16 z^7 a^{-5} +z^7 a^{-7} +3 a^4 z^6-4 a^2 z^6-32 z^6 a^{-2} -33 z^6 a^{-4} -13 z^6 a^{-6} -19 z^6+a^5 z^5-6 a^3 z^5-5 a z^5+30 z^5 a^{-1} +39 z^5 a^{-3} +8 z^5 a^{-5} -3 z^5 a^{-7} -5 a^4 z^4-3 a^2 z^4+46 z^4 a^{-2} +41 z^4 a^{-4} +13 z^4 a^{-6} +20 z^4-2 a^5 z^3+2 a^3 z^3+7 a z^3-7 z^3 a^{-1} -11 z^3 a^{-3} +2 z^3 a^{-5} +3 z^3 a^{-7} +3 a^4 z^2+4 a^2 z^2-23 z^2 a^{-2} -18 z^2 a^{-4} -5 z^2 a^{-6} -9 z^2+a^5 z-2 a z-z a^{-1} -z a^{-5} -z a^{-7} -a^4-a^2+4 a^{-2} +3 a^{-4} + a^{-6} +3 }[/math] |
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