K12a1167
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-5 q^5+14 q^4-26 q^3+38 q^2-47 q+51-47 q^{-1} +38 q^{-2} -26 q^{-3} +14 q^{-4} -5 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-10 t^3+35 t^2-68 t+85-68 t^{-1} +35 t^{-2} -10 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-2 z^6-5 z^4-2 z^2+1 }[/math] |
| Determinant | 313 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-2 a^2 z^6-2 z^6 a^{-2} +2 z^6+a^4 z^4-3 a^2 z^4-3 z^4 a^{-2} +z^4 a^{-4} -z^4+a^4 z^2+a^2 z^2+z^2 a^{-2} +z^2 a^{-4} -6 z^2+2 a^2+2 a^{-2} -3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 5 a z^{11}+5 z^{11} a^{-1} +15 a^2 z^{10}+15 z^{10} a^{-2} +30 z^{10}+19 a^3 z^9+33 a z^9+33 z^9 a^{-1} +19 z^9 a^{-3} +13 a^4 z^8-7 a^2 z^8-7 z^8 a^{-2} +13 z^8 a^{-4} -40 z^8+5 a^5 z^7-33 a^3 z^7-87 a z^7-87 z^7 a^{-1} -33 z^7 a^{-3} +5 z^7 a^{-5} +a^6 z^6-22 a^4 z^6-27 a^2 z^6-27 z^6 a^{-2} -22 z^6 a^{-4} +z^6 a^{-6} -8 z^6-6 a^5 z^5+22 a^3 z^5+64 a z^5+64 z^5 a^{-1} +22 z^5 a^{-3} -6 z^5 a^{-5} -a^6 z^4+15 a^4 z^4+23 a^2 z^4+23 z^4 a^{-2} +15 z^4 a^{-4} -z^4 a^{-6} +14 z^4+2 a^5 z^3-9 a^3 z^3-21 a z^3-21 z^3 a^{-1} -9 z^3 a^{-3} +2 z^3 a^{-5} -5 a^4 z^2-2 a^2 z^2-2 z^2 a^{-2} -5 z^2 a^{-4} +6 z^2+2 a^3 z+4 a z+4 z a^{-1} +2 z a^{-3} -2 a^2-2 a^{-2} -3 }[/math] |
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