K12a130
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+3 q^6-7 q^5+13 q^4-18 q^3+22 q^2-24 q+23-18 q^{-1} +13 q^{-2} -7 q^{-3} +3 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+14 t^2-36 t+49-36 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 | 153 |
| 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+3 a^2 z^2-z^2 a^{-2} +3 z^2 a^{-4} -z^2 a^{-6} -z^2-a^4+2 a^2- a^{-2} +2 a^{-4} - a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +6 z^{10} a^{-2} +3 z^{10} a^{-4} +3 z^{10}+5 a z^9+8 z^9 a^{-1} +7 z^9 a^{-3} +4 z^9 a^{-5} +6 a^2 z^8-4 z^8 a^{-2} -z^8 a^{-4} +3 z^8 a^{-6} +6 z^8+5 a^3 z^7+a z^7-12 z^7 a^{-1} -19 z^7 a^{-3} -10 z^7 a^{-5} +z^7 a^{-7} +3 a^4 z^6-5 a^2 z^6-15 z^6 a^{-2} -17 z^6 a^{-4} -11 z^6 a^{-6} -17 z^6+a^5 z^5-6 a^3 z^5-12 a z^5-6 z^5 a^{-1} +5 z^5 a^{-3} +2 z^5 a^{-5} -4 z^5 a^{-7} -5 a^4 z^4-a^2 z^4+16 z^4 a^{-2} +22 z^4 a^{-4} +13 z^4 a^{-6} +11 z^4-2 a^5 z^3+2 a^3 z^3+12 a z^3+12 z^3 a^{-1} +6 z^3 a^{-3} +7 z^3 a^{-5} +5 z^3 a^{-7} +3 a^4 z^2+4 a^2 z^2-7 z^2 a^{-2} -11 z^2 a^{-4} -6 z^2 a^{-6} -z^2+a^5 z-3 a z-3 z a^{-1} -2 z a^{-3} -3 z a^{-5} -2 z a^{-7} -a^4-2 a^2+ a^{-2} +2 a^{-4} + a^{-6} }[/math] |
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