K12n865
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 2 q^3-5 q^2+9 q-13+16 q^{-1} -16 q^{-2} +15 q^{-3} -12 q^{-4} +7 q^{-5} -3 q^{-6} + q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+4 t^3-11 t^2+21 t-25+21 t^{-1} -11 t^{-2} +4 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-4 z^6-7 z^4-3 z^2+1 }[/math] |
| Determinant | 99 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8+a^4 z^6-6 a^2 z^6+z^6+4 a^4 z^4-14 a^2 z^4+3 z^4+6 a^4 z^2-13 a^2 z^2+z^2 a^{-2} +3 z^2+2 a^4-3 a^2+ a^{-2} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^2 z^{10}+z^{10}+5 a^3 z^9+6 a z^9+z^9 a^{-1} +9 a^4 z^8+11 a^2 z^8+2 z^8+9 a^5 z^7-2 a^3 z^7-10 a z^7+z^7 a^{-1} +6 a^6 z^6-17 a^4 z^6-35 a^2 z^6+3 z^6 a^{-2} -9 z^6+3 a^7 z^5-15 a^5 z^5-14 a^3 z^5-6 a z^5-10 z^5 a^{-1} +a^8 z^4-6 a^6 z^4+15 a^4 z^4+34 a^2 z^4-9 z^4 a^{-2} +3 z^4-2 a^7 z^3+13 a^5 z^3+16 a^3 z^3+11 a z^3+10 z^3 a^{-1} -a^8 z^2+3 a^6 z^2-7 a^4 z^2-18 a^2 z^2+7 z^2 a^{-2} -3 a^5 z-5 a^3 z-4 a z-2 z a^{-1} +2 a^4+3 a^2- a^{-2} +1 }[/math] |
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