K12a1282
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^5-q^4+3 q^3-5 q^2+6 q-8+9 q^{-1} -9 q^{-2} +8 q^{-3} -6 q^{-4} +4 q^{-5} -2 q^{-6} + q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -6 t^2+16 t-19+16 t^{-1} -6 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ -6 z^4-8 z^2+1 }[/math] |
| Determinant | 63 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^6+a^6-z^4 a^4-z^2 a^4-2 z^4 a^2-3 z^2 a^2-2 z^4-4 z^2-1-z^4 a^{-2} -2 z^2 a^{-2} - a^{-2} +z^2 a^{-4} +2 a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +2 a^2 z^{10}+z^{10} a^{-2} +3 z^{10}+3 a^3 z^9-4 a z^9-6 z^9 a^{-1} +z^9 a^{-3} +3 a^4 z^8-8 a^2 z^8-4 z^8 a^{-2} +z^8 a^{-4} -16 z^8+3 a^5 z^7-12 a^3 z^7+8 a z^7+18 z^7 a^{-1} -5 z^7 a^{-3} +3 a^6 z^6-8 a^4 z^6+13 a^2 z^6+2 z^6 a^{-2} -7 z^6 a^{-4} +33 z^6+2 a^7 z^5-6 a^5 z^5+22 a^3 z^5-12 a z^5-36 z^5 a^{-1} +6 z^5 a^{-3} +a^8 z^4-6 a^6 z^4+10 a^4 z^4-8 a^2 z^4+4 z^4 a^{-2} +16 z^4 a^{-4} -37 z^4-3 a^7 z^3+6 a^5 z^3-16 a^3 z^3+7 a z^3+32 z^3 a^{-1} -2 a^8 z^2+5 a^6 z^2-2 a^4 z^2-2 a^2 z^2-3 z^2 a^{-2} -13 z^2 a^{-4} +17 z^2+3 a^3 z-3 a z-7 z a^{-1} -z a^{-3} -a^6+ a^{-2} +2 a^{-4} -1 }[/math] |
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