K12n809
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 2 q^7-3 q^6+3 q^5-4 q^4+3 q^3-2 q^2+q+1- q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^2+4 t-3+4 t^{-1} -2 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^4-4 z^2+1 }[/math] |
| Determinant | 15 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-2} +z^6 a^{-4} -7 z^4 a^{-2} +5 z^4 a^{-4} -z^4 a^{-6} +z^4-13 z^2 a^{-2} +8 z^2 a^{-4} -3 z^2 a^{-6} +4 z^2-6 a^{-2} +4 a^{-4} -2 a^{-6} + a^{-8} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^9 a^{-1} +z^9 a^{-3} +2 z^8 a^{-2} +2 z^8 a^{-4} +z^8 a^{-6} +z^8-7 z^7 a^{-1} -6 z^7 a^{-3} +2 z^7 a^{-5} +z^7 a^{-7} -16 z^6 a^{-2} -13 z^6 a^{-4} -4 z^6 a^{-6} -7 z^6+13 z^5 a^{-1} +6 z^5 a^{-3} -8 z^5 a^{-5} -z^5 a^{-7} +36 z^4 a^{-2} +26 z^4 a^{-4} +8 z^4 a^{-6} +3 z^4 a^{-8} +15 z^4-6 z^3 a^{-1} +8 z^3 a^{-3} +10 z^3 a^{-5} -4 z^3 a^{-7} -27 z^2 a^{-2} -16 z^2 a^{-4} -9 z^2 a^{-6} -7 z^2 a^{-8} -13 z^2-2 z a^{-1} -6 z a^{-3} -2 z a^{-5} +2 z a^{-7} +6 a^{-2} +4 a^{-4} +2 a^{-6} + a^{-8} +4 }[/math] |
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