K12n575
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{14}+q^{13}-2 q^{12}+2 q^{11}-q^{10}+q^9-q^7+2 q^6-q^5+q^4 }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-3 t^3+t^2+4 t-7+4 t^{-1} + t^{-2} -3 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+13 z^6+23 z^4+13 z^2+1 }[/math] |
| Determinant | 3 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-8} +z^8 a^{-10} +7 z^6 a^{-8} +7 z^6 a^{-10} -z^6 a^{-12} +15 z^4 a^{-8} +15 z^4 a^{-10} -7 z^4 a^{-12} +11 z^2 a^{-8} +13 z^2 a^{-10} -12 z^2 a^{-12} +z^2 a^{-14} + a^{-8} +5 a^{-10} -6 a^{-12} + a^{-14} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-10} +z^{10} a^{-12} +z^9 a^{-9} +2 z^9 a^{-11} +z^9 a^{-13} +z^8 a^{-8} -7 z^8 a^{-10} -8 z^8 a^{-12} -6 z^7 a^{-9} -14 z^7 a^{-11} -8 z^7 a^{-13} -7 z^6 a^{-8} +16 z^6 a^{-10} +22 z^6 a^{-12} +z^6 a^{-16} +9 z^5 a^{-9} +28 z^5 a^{-11} +20 z^5 a^{-13} +2 z^5 a^{-15} +z^5 a^{-17} +15 z^4 a^{-8} -20 z^4 a^{-10} -31 z^4 a^{-12} +z^4 a^{-14} -3 z^4 a^{-16} -3 z^3 a^{-9} -20 z^3 a^{-11} -19 z^3 a^{-13} -6 z^3 a^{-15} -4 z^3 a^{-17} -11 z^2 a^{-8} +17 z^2 a^{-10} +24 z^2 a^{-12} -3 z^2 a^{-14} +z^2 a^{-16} +7 z a^{-11} +5 z a^{-13} +2 z a^{-15} +4 z a^{-17} + a^{-8} -5 a^{-10} -6 a^{-12} - a^{-14} }[/math] |
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