K12a961
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-4 q^5+11 q^4-22 q^3+33 q^2-41 q+45-42 q^{-1} +35 q^{-2} -24 q^{-3} +13 q^{-4} -5 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-9 t^3+31 t^2-60 t+75-60 t^{-1} +31 t^{-2} -9 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-z^6-3 z^4-z^2+1 }[/math] |
| Determinant | 277 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-2 a^2 z^6-2 z^6 a^{-2} +3 z^6+a^4 z^4-4 a^2 z^4-5 z^4 a^{-2} +z^4 a^{-4} +4 z^4+a^4 z^2-2 a^2 z^2-5 z^2 a^{-2} +2 z^2 a^{-4} +3 z^2-2 a^{-2} + a^{-4} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 a z^{11}+4 z^{11} a^{-1} +13 a^2 z^{10}+11 z^{10} a^{-2} +24 z^{10}+17 a^3 z^9+28 a z^9+24 z^9 a^{-1} +13 z^9 a^{-3} +12 a^4 z^8-8 a^2 z^8-6 z^8 a^{-2} +9 z^8 a^{-4} -35 z^8+5 a^5 z^7-31 a^3 z^7-78 a z^7-68 z^7 a^{-1} -22 z^7 a^{-3} +4 z^7 a^{-5} +a^6 z^6-21 a^4 z^6-22 a^2 z^6-18 z^6 a^{-2} -16 z^6 a^{-4} +z^6 a^{-6} -z^6-7 a^5 z^5+19 a^3 z^5+65 a z^5+62 z^5 a^{-1} +16 z^5 a^{-3} -7 z^5 a^{-5} -a^6 z^4+12 a^4 z^4+22 a^2 z^4+24 z^4 a^{-2} +12 z^4 a^{-4} -2 z^4 a^{-6} +19 z^4+2 a^5 z^3-6 a^3 z^3-23 a z^3-25 z^3 a^{-1} -6 z^3 a^{-3} +4 z^3 a^{-5} -3 a^4 z^2-6 a^2 z^2-12 z^2 a^{-2} -5 z^2 a^{-4} +z^2 a^{-6} -9 z^2+a^3 z+3 a z+3 z a^{-1} -z a^{-5} +2 a^{-2} + a^{-4} +2 }[/math] |
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