K12a1209
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-4 q^5+8 q^4-15 q^3+22 q^2-26 q+29-26 q^{-1} +22 q^{-2} -15 q^{-3} +8 q^{-4} -4 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^5+5 t^4-12 t^3+22 t^2-32 t+37-32 t^{-1} +22 t^{-2} -12 t^{-3} +5 t^{-4} - t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^{10}-5 z^8-7 z^6+3 z^2+1 }[/math] |
| Determinant | 181 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^{10}+a^2 z^8+z^8 a^{-2} -7 z^8+5 a^2 z^6+5 z^6 a^{-2} -17 z^6+7 a^2 z^4+7 z^4 a^{-2} -14 z^4+3 z^2-3 a^2-3 a^{-2} +7 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a z^{11}+3 z^{11} a^{-1} +7 a^2 z^{10}+7 z^{10} a^{-2} +14 z^{10}+8 a^3 z^9+2 a z^9+2 z^9 a^{-1} +8 z^9 a^{-3} +7 a^4 z^8-16 a^2 z^8-16 z^8 a^{-2} +7 z^8 a^{-4} -46 z^8+4 a^5 z^7-17 a^3 z^7-16 a z^7-16 z^7 a^{-1} -17 z^7 a^{-3} +4 z^7 a^{-5} +a^6 z^6-17 a^4 z^6+18 a^2 z^6+18 z^6 a^{-2} -17 z^6 a^{-4} +z^6 a^{-6} +72 z^6-10 a^5 z^5+7 a^3 z^5+22 a z^5+22 z^5 a^{-1} +7 z^5 a^{-3} -10 z^5 a^{-5} -2 a^6 z^4+10 a^4 z^4-10 a^2 z^4-10 z^4 a^{-2} +10 z^4 a^{-4} -2 z^4 a^{-6} -44 z^4+5 a^5 z^3+5 a^3 z^3-4 a z^3-4 z^3 a^{-1} +5 z^3 a^{-3} +5 z^3 a^{-5} -a^4 z^2-a^2 z^2-z^2 a^{-2} -z^2 a^{-4} -3 a^3 z-6 a z-6 z a^{-1} -3 z a^{-3} +3 a^2+3 a^{-2} +7 }[/math] |
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