K12a674
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-4 q^5+10 q^4-18 q^3+27 q^2-33 q+35-33 q^{-1} +27 q^{-2} -18 q^{-3} +10 q^{-4} -4 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+25 t^2-47 t+59-47 t^{-1} +25 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-3 z^4-3 z^2+1 }[/math] |
| Determinant | 221 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-2 a^2 z^6-2 z^6 a^{-2} +4 z^6+a^4 z^4-6 a^2 z^4-6 z^4 a^{-2} +z^4 a^{-4} +7 z^4+2 a^4 z^2-6 a^2 z^2-6 z^2 a^{-2} +2 z^2 a^{-4} +5 z^2+a^4-a^2- a^{-2} + a^{-4} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +6 a^2 z^{10}+7 z^{10} a^{-2} +13 z^{10}+9 a^3 z^9+17 a z^9+18 z^9 a^{-1} +10 z^9 a^{-3} +8 a^4 z^8+6 a^2 z^8-z^8 a^{-2} +8 z^8 a^{-4} -11 z^8+4 a^5 z^7-11 a^3 z^7-37 a z^7-44 z^7 a^{-1} -18 z^7 a^{-3} +4 z^7 a^{-5} +a^6 z^6-16 a^4 z^6-32 a^2 z^6-17 z^6 a^{-2} -16 z^6 a^{-4} +z^6 a^{-6} -15 z^6-8 a^5 z^5-2 a^3 z^5+22 a z^5+37 z^5 a^{-1} +13 z^5 a^{-3} -8 z^5 a^{-5} -2 a^6 z^4+12 a^4 z^4+29 a^2 z^4+18 z^4 a^{-2} +11 z^4 a^{-4} -2 z^4 a^{-6} +20 z^4+5 a^5 z^3+5 a^3 z^3-4 a z^3-15 z^3 a^{-1} -7 z^3 a^{-3} +4 z^3 a^{-5} +a^6 z^2-5 a^4 z^2-10 a^2 z^2-8 z^2 a^{-2} -4 z^2 a^{-4} +z^2 a^{-6} -7 z^2-a^5 z-a^3 z+2 z a^{-1} +2 z a^{-3} +a^4+a^2+ a^{-2} + a^{-4} +1 }[/math] |
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