K12a1188
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-6 q^5+16 q^4-29 q^3+43 q^2-53 q+57-53 q^{-1} +43 q^{-2} -29 q^{-3} +16 q^{-4} -6 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-9 t^3+36 t^2-79 t+103-79 t^{-1} +36 t^{-2} -9 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-z^6+2 z^4+1 }[/math] |
| Determinant | 353 |
| 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^4-3 a^2 z^4-3 z^4 a^{-2} +z^4 a^{-4} +6 z^4-2 a^2 z^2-2 z^2 a^{-2} +4 z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 7 a z^{11}+7 z^{11} a^{-1} +20 a^2 z^{10}+20 z^{10} a^{-2} +40 z^{10}+24 a^3 z^9+39 a z^9+39 z^9 a^{-1} +24 z^9 a^{-3} +16 a^4 z^8-14 a^2 z^8-14 z^8 a^{-2} +16 z^8 a^{-4} -60 z^8+6 a^5 z^7-39 a^3 z^7-108 a z^7-108 z^7 a^{-1} -39 z^7 a^{-3} +6 z^7 a^{-5} +a^6 z^6-23 a^4 z^6-28 a^2 z^6-28 z^6 a^{-2} -23 z^6 a^{-4} +z^6 a^{-6} -8 z^6-5 a^5 z^5+17 a^3 z^5+72 a z^5+72 z^5 a^{-1} +17 z^5 a^{-3} -5 z^5 a^{-5} +8 a^4 z^4+27 a^2 z^4+27 z^4 a^{-2} +8 z^4 a^{-4} +38 z^4-a^3 z^3-8 a z^3-8 z^3 a^{-1} -z^3 a^{-3} -6 a^2 z^2-6 z^2 a^{-2} -12 z^2-a^3 z-3 a z-3 z a^{-1} -z a^{-3} +1 }[/math] |
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