K12a1273
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-2 q^5+3 q^4-5 q^3+7 q^2-8 q+9-8 q^{-1} +7 q^{-2} -5 q^{-3} +3 q^{-4} -2 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^5+3 t^4-5 t^3+7 t^2-9 t+11-9 t^{-1} +7 t^{-2} -5 t^{-3} +3 t^{-4} - t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^{10}-7 z^8-16 z^6-13 z^4-3 z^2+1 }[/math] |
| Determinant | 61 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^{10}+a^2 z^8+z^8 a^{-2} -9 z^8+7 a^2 z^6+7 z^6 a^{-2} -30 z^6+16 a^2 z^4+16 z^4 a^{-2} -45 z^4+13 a^2 z^2+13 z^2 a^{-2} -29 z^2+3 a^2+3 a^{-2} -5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +2 a^2 z^{10}+2 z^{10} a^{-2} +4 z^{10}+2 a^3 z^9-4 a z^9-4 z^9 a^{-1} +2 z^9 a^{-3} +2 a^4 z^8-11 a^2 z^8-11 z^8 a^{-2} +2 z^8 a^{-4} -26 z^8+2 a^5 z^7-8 a^3 z^7+3 a z^7+3 z^7 a^{-1} -8 z^7 a^{-3} +2 z^7 a^{-5} +a^6 z^6-7 a^4 z^6+25 a^2 z^6+25 z^6 a^{-2} -7 z^6 a^{-4} +z^6 a^{-6} +66 z^6-8 a^5 z^5+10 a^3 z^5+9 a z^5+9 z^5 a^{-1} +10 z^5 a^{-3} -8 z^5 a^{-5} -4 a^6 z^4+5 a^4 z^4-27 a^2 z^4-27 z^4 a^{-2} +5 z^4 a^{-4} -4 z^4 a^{-6} -72 z^4+7 a^5 z^3-5 a^3 z^3-10 a z^3-10 z^3 a^{-1} -5 z^3 a^{-3} +7 z^3 a^{-5} +3 a^6 z^2-a^4 z^2+14 a^2 z^2+14 z^2 a^{-2} -z^2 a^{-4} +3 z^2 a^{-6} +36 z^2-a^5 z+2 a z+2 z a^{-1} -z a^{-5} -3 a^2-3 a^{-2} -5 }[/math] |
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