K12n468
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+2 q^6-3 q^5+4 q^4-5 q^3+6 q^2-5 q+5-3 q^{-1} +2 q^{-2} - q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-3 t^3+5 t^2-6 t+7-6 t^{-1} +5 t^{-2} -3 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+5 z^6+7 z^4+3 z^2+1 }[/math] |
| Determinant | 37 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-2} +7 z^6 a^{-2} -z^6 a^{-4} -z^6+17 z^4 a^{-2} -5 z^4 a^{-4} -5 z^4+17 z^2 a^{-2} -7 z^2 a^{-4} -7 z^2+6 a^{-2} -3 a^{-4} -2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10} a^{-4} +z^9 a^{-1} +3 z^9 a^{-3} +2 z^9 a^{-5} -6 z^8 a^{-2} -4 z^8 a^{-4} +2 z^8 a^{-6} -5 z^7 a^{-1} -16 z^7 a^{-3} -10 z^7 a^{-5} +z^7 a^{-7} +18 z^6 a^{-2} +5 z^6 a^{-4} -10 z^6 a^{-6} +3 z^6+2 a z^5+13 z^5 a^{-1} +31 z^5 a^{-3} +15 z^5 a^{-5} -5 z^5 a^{-7} +2 a^2 z^4-29 z^4 a^{-2} -7 z^4 a^{-4} +13 z^4 a^{-6} -7 z^4+a^3 z^3-a z^3-14 z^3 a^{-1} -28 z^3 a^{-3} -10 z^3 a^{-5} +6 z^3 a^{-7} -2 a^2 z^2+21 z^2 a^{-2} +7 z^2 a^{-4} -4 z^2 a^{-6} +8 z^2-a^3 z+5 z a^{-1} +8 z a^{-3} +3 z a^{-5} -z a^{-7} -6 a^{-2} -3 a^{-4} -2 }[/math] |
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