K12a76
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{11}-4 q^{10}+7 q^9-12 q^8+17 q^7-20 q^6+22 q^5-20 q^4+17 q^3-12 q^2+7 q-3+ q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -8 t^2+36 t-55+36 t^{-1} -8 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ -8 z^4+4 z^2+1 }[/math] |
| Determinant | 143 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^{-2} -3 z^4 a^{-4} -3 z^4 a^{-6} -z^4 a^{-8} +2 z^2 a^{-2} -z^2 a^{-4} -z^2 a^{-6} +2 z^2 a^{-8} +z^2 a^{-10} +z^2+ a^{-2} + a^{-8} - a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-7} +2 z^{11} a^{-9} +6 z^{10} a^{-6} +11 z^{10} a^{-8} +5 z^{10} a^{-10} +9 z^9 a^{-5} +8 z^9 a^{-7} +3 z^9 a^{-9} +4 z^9 a^{-11} +10 z^8 a^{-4} -8 z^8 a^{-6} -40 z^8 a^{-8} -21 z^8 a^{-10} +z^8 a^{-12} +9 z^7 a^{-3} -16 z^7 a^{-5} -46 z^7 a^{-7} -40 z^7 a^{-9} -19 z^7 a^{-11} +6 z^6 a^{-2} -16 z^6 a^{-4} -10 z^6 a^{-6} +40 z^6 a^{-8} +24 z^6 a^{-10} -4 z^6 a^{-12} +3 z^5 a^{-1} -13 z^5 a^{-3} +5 z^5 a^{-5} +58 z^5 a^{-7} +64 z^5 a^{-9} +27 z^5 a^{-11} -6 z^4 a^{-2} +7 z^4 a^{-4} +12 z^4 a^{-6} -12 z^4 a^{-8} -6 z^4 a^{-10} +4 z^4 a^{-12} +z^4-2 z^3 a^{-1} +9 z^3 a^{-3} -z^3 a^{-5} -32 z^3 a^{-7} -31 z^3 a^{-9} -11 z^3 a^{-11} +4 z^2 a^{-2} -5 z^2 a^{-6} -z^2 a^{-10} -z^2 a^{-12} -z^2-z a^{-3} +6 z a^{-7} +4 z a^{-9} -z a^{-11} - a^{-2} + a^{-8} + a^{-10} }[/math] |
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