K12a373
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{13}-4 q^{12}+8 q^{11}-13 q^{10}+18 q^9-22 q^8+22 q^7-20 q^6+17 q^5-11 q^4+7 q^3-3 q^2+q }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-18 t^2+30 t-35+30 t^{-1} -18 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6+4 z^4+5 z^2+1 }[/math] |
| Determinant | 147 |
| 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} -9 z^4 a^{-6} +12 z^4 a^{-8} -3 z^4 a^{-10} +5 z^2 a^{-4} -7 z^2 a^{-6} +14 z^2 a^{-8} -8 z^2 a^{-10} +z^2 a^{-12} +2 a^{-4} -2 a^{-6} +4 a^{-8} -4 a^{-10} + a^{-12} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +3 z^{10} a^{-6} +7 z^{10} a^{-8} +4 z^{10} a^{-10} +3 z^9 a^{-5} +7 z^9 a^{-7} +12 z^9 a^{-9} +8 z^9 a^{-11} +z^8 a^{-4} -8 z^8 a^{-6} -12 z^8 a^{-8} +8 z^8 a^{-10} +11 z^8 a^{-12} -14 z^7 a^{-5} -38 z^7 a^{-7} -37 z^7 a^{-9} -2 z^7 a^{-11} +11 z^7 a^{-13} -5 z^6 a^{-4} -5 z^6 a^{-6} -23 z^6 a^{-8} -43 z^6 a^{-10} -12 z^6 a^{-12} +8 z^6 a^{-14} +21 z^5 a^{-5} +47 z^5 a^{-7} +15 z^5 a^{-9} -28 z^5 a^{-11} -13 z^5 a^{-13} +4 z^5 a^{-15} +9 z^4 a^{-4} +25 z^4 a^{-6} +49 z^4 a^{-8} +39 z^4 a^{-10} -2 z^4 a^{-12} -7 z^4 a^{-14} +z^4 a^{-16} -10 z^3 a^{-5} -16 z^3 a^{-7} +13 z^3 a^{-9} +27 z^3 a^{-11} +6 z^3 a^{-13} -2 z^3 a^{-15} -7 z^2 a^{-4} -16 z^2 a^{-6} -25 z^2 a^{-8} -17 z^2 a^{-10} +z^2 a^{-12} +2 z^2 a^{-14} +z a^{-7} -5 z a^{-9} -8 z a^{-11} -2 z a^{-13} +2 a^{-4} +2 a^{-6} +4 a^{-8} +4 a^{-10} + a^{-12} }[/math] |
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