K12a657
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+4 q^6-9 q^5+15 q^4-22 q^3+27 q^2-28 q+27-21 q^{-1} +15 q^{-2} -8 q^{-3} +3 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-9 t^3+22 t^2-36 t+43-36 t^{-1} +22 t^{-2} -9 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+7 z^6+8 z^4+3 z^2+1 }[/math] |
| Determinant | 181 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-2} +z^8-a^2 z^6+4 z^6 a^{-2} -z^6 a^{-4} +5 z^6-4 a^2 z^4+4 z^4 a^{-2} -3 z^4 a^{-4} +11 z^4-6 a^2 z^2-2 z^2 a^{-2} -2 z^2 a^{-4} +13 z^2-3 a^2-3 a^{-2} +7 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-1} +2 z^{11} a^{-3} +11 z^{10} a^{-2} +6 z^{10} a^{-4} +5 z^{10}+8 a z^9+9 z^9 a^{-1} +8 z^9 a^{-3} +7 z^9 a^{-5} +9 a^2 z^8-22 z^8 a^{-2} -14 z^8 a^{-4} +4 z^8 a^{-6} +5 z^8+6 a^3 z^7-6 a z^7-19 z^7 a^{-1} -31 z^7 a^{-3} -23 z^7 a^{-5} +z^7 a^{-7} +3 a^4 z^6-16 a^2 z^6+11 z^6 a^{-2} +8 z^6 a^{-4} -13 z^6 a^{-6} -29 z^6+a^5 z^5-8 a^3 z^5-9 a z^5-2 z^5 a^{-1} +24 z^5 a^{-3} +23 z^5 a^{-5} -3 z^5 a^{-7} -4 a^4 z^4+19 a^2 z^4-2 z^4 a^{-2} -5 z^4 a^{-4} +11 z^4 a^{-6} +37 z^4-2 a^5 z^3+5 a^3 z^3+19 a z^3+17 z^3 a^{-1} -5 z^3 a^{-3} -8 z^3 a^{-5} +2 z^3 a^{-7} +a^4 z^2-12 a^2 z^2-5 z^2 a^{-2} +3 z^2 a^{-4} -z^2 a^{-6} -22 z^2+a^5 z-2 a^3 z-8 a z-8 z a^{-1} -2 z a^{-3} +z a^{-5} +3 a^2+3 a^{-2} +7 }[/math] |
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