K12a725
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-2 q^{11}+4 q^{10}-9 q^9+12 q^8-16 q^7+19 q^6-17 q^5+15 q^4-11 q^3+7 q^2-3 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+16 t^2-25 t+27-25 t^{-1} +16 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-8 z^4+3 z^2+1 }[/math] |
| Determinant | 117 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -2 z^6 a^{-6} -z^6 a^{-8} +z^4 a^{-2} -z^4 a^{-4} -6 z^4 a^{-6} -3 z^4 a^{-8} +z^4 a^{-10} +2 z^2 a^{-2} +4 z^2 a^{-4} -3 z^2 a^{-6} -3 z^2 a^{-8} +3 z^2 a^{-10} +2 a^{-4} + a^{-6} -3 a^{-8} + a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +3 z^{10} a^{-6} +5 z^{10} a^{-8} +2 z^{10} a^{-10} +5 z^9 a^{-5} +3 z^9 a^{-7} +2 z^9 a^{-11} +5 z^8 a^{-4} -4 z^8 a^{-6} -16 z^8 a^{-8} -5 z^8 a^{-10} +2 z^8 a^{-12} +3 z^7 a^{-3} -13 z^7 a^{-5} -12 z^7 a^{-7} -2 z^7 a^{-11} +2 z^7 a^{-13} +z^6 a^{-2} -14 z^6 a^{-4} -2 z^6 a^{-6} +31 z^6 a^{-8} +14 z^6 a^{-10} -3 z^6 a^{-12} +z^6 a^{-14} -8 z^5 a^{-3} +12 z^5 a^{-5} +18 z^5 a^{-7} +2 z^5 a^{-9} -3 z^5 a^{-11} -7 z^5 a^{-13} -3 z^4 a^{-2} +12 z^4 a^{-4} +6 z^4 a^{-6} -31 z^4 a^{-8} -21 z^4 a^{-10} -3 z^4 a^{-12} -4 z^4 a^{-14} +4 z^3 a^{-3} -7 z^3 a^{-5} -10 z^3 a^{-7} +7 z^3 a^{-11} +8 z^3 a^{-13} +2 z^2 a^{-2} -8 z^2 a^{-4} -2 z^2 a^{-6} +20 z^2 a^{-8} +12 z^2 a^{-10} +4 z^2 a^{-12} +4 z^2 a^{-14} +3 z a^{-7} -z a^{-9} -8 z a^{-11} -4 z a^{-13} +2 a^{-4} - a^{-6} -3 a^{-8} - a^{-10} }[/math] |
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