K12a158
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{13}-3 q^{12}+6 q^{11}-11 q^{10}+14 q^9-17 q^8+18 q^7-16 q^6+14 q^5-9 q^4+6 q^3-3 q^2+q }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-16 t^2+23 t-25+23 t^{-1} -16 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6+6 z^4+6 z^2+1 }[/math] |
| Determinant | 119 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-6} +z^6 a^{-4} -5 z^6 a^{-6} +3 z^6 a^{-8} +4 z^4 a^{-4} -8 z^4 a^{-6} +13 z^4 a^{-8} -3 z^4 a^{-10} +4 z^2 a^{-4} -5 z^2 a^{-6} +16 z^2 a^{-8} -10 z^2 a^{-10} +z^2 a^{-12} + a^{-4} - a^{-6} +6 a^{-8} -7 a^{-10} +2 a^{-12} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +3 z^{10} a^{-6} +6 z^{10} a^{-8} +3 z^{10} a^{-10} +3 z^9 a^{-5} +4 z^9 a^{-7} +6 z^9 a^{-9} +5 z^9 a^{-11} +z^8 a^{-4} -11 z^8 a^{-6} -17 z^8 a^{-8} +2 z^8 a^{-10} +7 z^8 a^{-12} -15 z^7 a^{-5} -30 z^7 a^{-7} -23 z^7 a^{-9} -z^7 a^{-11} +7 z^7 a^{-13} -5 z^6 a^{-4} +6 z^6 a^{-6} +3 z^6 a^{-8} -22 z^6 a^{-10} -9 z^6 a^{-12} +5 z^6 a^{-14} +23 z^5 a^{-5} +44 z^5 a^{-7} +13 z^5 a^{-9} -20 z^5 a^{-11} -9 z^5 a^{-13} +3 z^5 a^{-15} +8 z^4 a^{-4} +10 z^4 a^{-6} +19 z^4 a^{-8} +25 z^4 a^{-10} +3 z^4 a^{-12} -4 z^4 a^{-14} +z^4 a^{-16} -11 z^3 a^{-5} -21 z^3 a^{-7} +5 z^3 a^{-9} +24 z^3 a^{-11} +6 z^3 a^{-13} -3 z^3 a^{-15} -5 z^2 a^{-4} -7 z^2 a^{-6} -18 z^2 a^{-8} -19 z^2 a^{-10} -z^2 a^{-12} +z^2 a^{-14} -z^2 a^{-16} +z a^{-5} +3 z a^{-7} -6 z a^{-9} -10 z a^{-11} -z a^{-13} +z a^{-15} + a^{-4} + a^{-6} +6 a^{-8} +7 a^{-10} +2 a^{-12} }[/math] |
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