K12a952
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{13}-3 q^{12}+6 q^{11}-10 q^{10}+14 q^9-18 q^8+18 q^7-17 q^6+15 q^5-10 q^4+7 q^3-3 q^2+q }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+9 t^3-17 t^2+22 t-23+22 t^{-1} -17 t^{-2} +9 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-7 z^6-3 z^4+3 z^2+1 }[/math] |
| Determinant | 123 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-6} -z^8 a^{-8} +z^6 a^{-4} -4 z^6 a^{-6} -5 z^6 a^{-8} +z^6 a^{-10} +4 z^4 a^{-4} -2 z^4 a^{-6} -9 z^4 a^{-8} +4 z^4 a^{-10} +4 z^2 a^{-4} +5 z^2 a^{-6} -10 z^2 a^{-8} +4 z^2 a^{-10} + a^{-4} +4 a^{-6} -6 a^{-8} +2 a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-7} +2 z^{11} a^{-9} +4 z^{10} a^{-6} +10 z^{10} a^{-8} +6 z^{10} a^{-10} +3 z^9 a^{-5} -z^9 a^{-7} +4 z^9 a^{-9} +8 z^9 a^{-11} +z^8 a^{-4} -17 z^8 a^{-6} -43 z^8 a^{-8} -17 z^8 a^{-10} +8 z^8 a^{-12} -14 z^7 a^{-5} -24 z^7 a^{-7} -38 z^7 a^{-9} -21 z^7 a^{-11} +7 z^7 a^{-13} -5 z^6 a^{-4} +20 z^6 a^{-6} +62 z^6 a^{-8} +16 z^6 a^{-10} -16 z^6 a^{-12} +5 z^6 a^{-14} +19 z^5 a^{-5} +46 z^5 a^{-7} +60 z^5 a^{-9} +19 z^5 a^{-11} -11 z^5 a^{-13} +3 z^5 a^{-15} +8 z^4 a^{-4} -10 z^4 a^{-6} -47 z^4 a^{-8} -12 z^4 a^{-10} +11 z^4 a^{-12} -5 z^4 a^{-14} +z^4 a^{-16} -8 z^3 a^{-5} -32 z^3 a^{-7} -42 z^3 a^{-9} -7 z^3 a^{-11} +8 z^3 a^{-13} -3 z^3 a^{-15} -5 z^2 a^{-4} +8 z^2 a^{-6} +22 z^2 a^{-8} +6 z^2 a^{-10} -z^2 a^{-12} +z^2 a^{-14} -z^2 a^{-16} +z a^{-5} +10 z a^{-7} +12 z a^{-9} +z a^{-11} -2 z a^{-13} + a^{-4} -4 a^{-6} -6 a^{-8} -2 a^{-10} }[/math] |
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