K12a515
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+4 q^6-9 q^5+15 q^4-21 q^3+26 q^2-27 q+26-21 q^{-1} +14 q^{-2} -8 q^{-3} +4 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+21 t^2-37 t+45-37 t^{-1} +21 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6-z^4+1 }[/math] |
| Determinant | 177 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-a^2 z^6-3 z^6 a^{-2} +5 z^6-3 a^2 z^4-11 z^4 a^{-2} +3 z^4 a^{-4} +10 z^4-2 a^2 z^2-12 z^2 a^{-2} +7 z^2 a^{-4} -z^2 a^{-6} +8 z^2-3 a^{-2} +3 a^{-4} - a^{-6} +2 }[/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+15 z^9 a^{-1} +14 z^9 a^{-3} +6 z^9 a^{-5} +8 a^2 z^8-2 z^8 a^{-2} +z^8 a^{-4} +4 z^8 a^{-6} +9 z^8+7 a^3 z^7-a z^7-34 z^7 a^{-1} -43 z^7 a^{-3} -16 z^7 a^{-5} +z^7 a^{-7} +4 a^4 z^6-7 a^2 z^6-40 z^6 a^{-2} -32 z^6 a^{-4} -13 z^6 a^{-6} -32 z^6+a^5 z^5-10 a^3 z^5-15 a z^5+15 z^5 a^{-1} +30 z^5 a^{-3} +8 z^5 a^{-5} -3 z^5 a^{-7} -6 a^4 z^4-2 a^2 z^4+53 z^4 a^{-2} +40 z^4 a^{-4} +13 z^4 a^{-6} +30 z^4-a^5 z^3+5 a^3 z^3+16 a z^3+9 z^3 a^{-1} -z^3 a^{-3} +3 z^3 a^{-5} +3 z^3 a^{-7} +2 a^4 z^2+2 a^2 z^2-24 z^2 a^{-2} -18 z^2 a^{-4} -5 z^2 a^{-6} -11 z^2-a^3 z-4 a z-5 z a^{-1} -3 z a^{-3} -2 z a^{-5} -z a^{-7} +3 a^{-2} +3 a^{-4} + a^{-6} +2 }[/math] |
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