K12a758
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^8-3 q^7+5 q^6-9 q^5+13 q^4-15 q^3+17 q^2-16 q+14-10 q^{-1} +6 q^{-2} -3 q^{-3} + q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+13 t^2-25 t+31-25 t^{-1} +13 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^6-5 z^4+1 }[/math] |
| Determinant | 113 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-2} -z^6 a^{-4} -z^6+a^2 z^4-z^4 a^{-2} -3 z^4 a^{-4} +z^4 a^{-6} -3 z^4+2 a^2 z^2+3 z^2 a^{-2} -3 z^2 a^{-4} +2 z^2 a^{-6} -4 z^2+a^2+3 a^{-2} - a^{-4} -2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +3 z^{10} a^{-2} +6 z^{10} a^{-4} +3 z^{10} a^{-6} +5 z^9 a^{-1} +5 z^9 a^{-3} +3 z^9 a^{-5} +3 z^9 a^{-7} -z^8 a^{-2} -21 z^8 a^{-4} -13 z^8 a^{-6} +z^8 a^{-8} +6 z^8+6 a z^7-5 z^7 a^{-1} -22 z^7 a^{-3} -27 z^7 a^{-5} -16 z^7 a^{-7} +5 a^2 z^6-9 z^6 a^{-2} +22 z^6 a^{-4} +16 z^6 a^{-6} -5 z^6 a^{-8} -5 z^6+3 a^3 z^5-5 a z^5-5 z^5 a^{-1} +19 z^5 a^{-3} +43 z^5 a^{-5} +27 z^5 a^{-7} +a^4 z^4-5 a^2 z^4-14 z^4 a^{-4} -6 z^4 a^{-6} +7 z^4 a^{-8} -5 z^4-3 a^3 z^3+4 z^3 a^{-1} -7 z^3 a^{-3} -23 z^3 a^{-5} -15 z^3 a^{-7} -a^4 z^2+3 a^2 z^2+7 z^2 a^{-2} +7 z^2 a^{-4} +z^2 a^{-6} -2 z^2 a^{-8} +7 z^2+a^3 z+a z+2 z a^{-3} +3 z a^{-5} +z a^{-7} -a^2-3 a^{-2} - a^{-4} -2 }[/math] |
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