K12a893
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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+50-46 q^{-1} +38 q^{-2} -25 q^{-3} +13 q^{-4} -5 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-9 t^3+33 t^2-68 t+87-68 t^{-1} +33 t^{-2} -9 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-z^6-z^4-z^2+1 }[/math] |
| Determinant | 309 |
| 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^4-4 z^4 a^{-2} +z^4 a^{-4} +5 z^4+a^4 z^2-3 a^2 z^2-4 z^2 a^{-2} +z^2 a^{-4} +4 z^2-2 a^{-2} + a^{-4} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 5 a z^{11}+5 z^{11} a^{-1} +14 a^2 z^{10}+16 z^{10} a^{-2} +30 z^{10}+17 a^3 z^9+31 a z^9+34 z^9 a^{-1} +20 z^9 a^{-3} +12 a^4 z^8-5 a^2 z^8-13 z^8 a^{-2} +13 z^8 a^{-4} -43 z^8+5 a^5 z^7-26 a^3 z^7-84 a z^7-97 z^7 a^{-1} -39 z^7 a^{-3} +5 z^7 a^{-5} +a^6 z^6-20 a^4 z^6-29 a^2 z^6-20 z^6 a^{-2} -22 z^6 a^{-4} +z^6 a^{-6} -5 z^6-7 a^5 z^5+12 a^3 z^5+66 a z^5+84 z^5 a^{-1} +31 z^5 a^{-3} -6 z^5 a^{-5} -a^6 z^4+13 a^4 z^4+28 a^2 z^4+27 z^4 a^{-2} +14 z^4 a^{-4} -z^4 a^{-6} +26 z^4+3 a^5 z^3-2 a^3 z^3-24 a z^3-33 z^3 a^{-1} -13 z^3 a^{-3} +z^3 a^{-5} -3 a^4 z^2-9 a^2 z^2-12 z^2 a^{-2} -5 z^2 a^{-4} -13 z^2+a^3 z+4 a z+6 z a^{-1} +3 z a^{-3} +2 a^{-2} + a^{-4} +2 }[/math] |
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