K12a221
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+4 q^6-8 q^5+14 q^4-20 q^3+24 q^2-26 q+25-20 q^{-1} +14 q^{-2} -8 q^{-3} +4 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+14 t^2-40 t+57-40 t^{-1} +14 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+2 z^4-2 z^2+1 }[/math] |
| Determinant | 169 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-2} -z^6+2 a^2 z^4-z^4 a^{-2} +2 z^4 a^{-4} -z^4-a^4 z^2+2 a^2 z^2-2 z^2 a^{-2} +2 z^2 a^{-4} -z^2 a^{-6} -2 z^2+a^2- a^{-2} + a^{-4} }[/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}+7 a z^9+14 z^9 a^{-1} +13 z^9 a^{-3} +6 z^9 a^{-5} +8 a^2 z^8-8 z^8 a^{-2} -2 z^8 a^{-4} +4 z^8 a^{-6} +6 z^8+7 a^3 z^7-4 a z^7-38 z^7 a^{-1} -47 z^7 a^{-3} -19 z^7 a^{-5} +z^7 a^{-7} +4 a^4 z^6-8 a^2 z^6-21 z^6 a^{-2} -24 z^6 a^{-4} -14 z^6 a^{-6} -23 z^6+a^5 z^5-10 a^3 z^5-5 a z^5+37 z^5 a^{-1} +51 z^5 a^{-3} +17 z^5 a^{-5} -3 z^5 a^{-7} -6 a^4 z^4-a^2 z^4+33 z^4 a^{-2} +33 z^4 a^{-4} +14 z^4 a^{-6} +19 z^4-a^5 z^3+4 a^3 z^3+3 a z^3-19 z^3 a^{-1} -25 z^3 a^{-3} -6 z^3 a^{-5} +2 z^3 a^{-7} +2 a^4 z^2+3 a^2 z^2-14 z^2 a^{-2} -13 z^2 a^{-4} -4 z^2 a^{-6} -4 z^2+a z+5 z a^{-1} +5 z a^{-3} +z a^{-5} -a^2+ a^{-2} + a^{-4} }[/math] |
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