K12a775
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{11}-2 q^{10}+4 q^9-7 q^8+9 q^7-12 q^6+13 q^5-12 q^4+11 q^3-8 q^2+5 q-2+ q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -6 t^2+22 t-31+22 t^{-1} -6 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ -6 z^4-2 z^2+1 }[/math] |
| Determinant | 87 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^{-2} -2 z^4 a^{-4} -2 z^4 a^{-6} -z^4 a^{-8} -z^2 a^{-4} -2 z^2 a^{-6} -z^2 a^{-8} +z^2 a^{-10} +z^2+ a^{-4} - a^{-6} - a^{-8} + a^{-10} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +2 z^{10} a^{-6} +4 z^{10} a^{-8} +2 z^{10} a^{-10} +3 z^9 a^{-5} -z^9 a^{-7} -2 z^9 a^{-9} +2 z^9 a^{-11} +4 z^8 a^{-4} -2 z^8 a^{-6} -16 z^8 a^{-8} -9 z^8 a^{-10} +z^8 a^{-12} +4 z^7 a^{-3} -3 z^7 a^{-5} +z^7 a^{-7} -3 z^7 a^{-9} -11 z^7 a^{-11} +3 z^6 a^{-2} -6 z^6 a^{-4} -4 z^6 a^{-6} +22 z^6 a^{-8} +11 z^6 a^{-10} -6 z^6 a^{-12} +2 z^5 a^{-1} -5 z^5 a^{-3} -4 z^5 a^{-5} -12 z^5 a^{-7} +4 z^5 a^{-9} +19 z^5 a^{-11} -2 z^4 a^{-2} +5 z^4 a^{-4} +5 z^4 a^{-6} -18 z^4 a^{-8} -4 z^4 a^{-10} +11 z^4 a^{-12} +z^4-2 z^3 a^{-1} +4 z^3 a^{-3} +7 z^3 a^{-5} +13 z^3 a^{-7} -12 z^3 a^{-11} -2 z^2 a^{-4} -5 z^2 a^{-6} +7 z^2 a^{-8} +2 z^2 a^{-10} -6 z^2 a^{-12} -2 z^2-3 z a^{-5} -5 z a^{-7} +z a^{-9} +3 z a^{-11} + a^{-4} + a^{-6} - a^{-8} - a^{-10} +1 }[/math] |
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