K12a1068
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^8-3 q^7+7 q^6-12 q^5+17 q^4-21 q^3+22 q^2-21 q+18-12 q^{-1} +7 q^{-2} -3 q^{-3} + q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+16 t^2-32 t+41-32 t^{-1} +16 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-8 z^4-4 z^2+1 }[/math] |
| Determinant | 145 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -2 z^6 a^{-2} -z^6 a^{-4} -z^6+a^2 z^4-6 z^4 a^{-2} -2 z^4 a^{-4} +z^4 a^{-6} -2 z^4+2 a^2 z^2-6 z^2 a^{-2} -z^2 a^{-4} +2 z^2 a^{-6} -z^2+a^2-2 a^{-2} + a^{-6} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +6 z^{10} a^{-2} +10 z^{10} a^{-4} +4 z^{10} a^{-6} +10 z^9 a^{-1} +7 z^9 a^{-3} +3 z^9 a^{-7} -6 z^8 a^{-2} -34 z^8 a^{-4} -16 z^8 a^{-6} +z^8 a^{-8} +11 z^8+9 a z^7-20 z^7 a^{-1} -36 z^7 a^{-3} -21 z^7 a^{-5} -14 z^7 a^{-7} +6 a^2 z^6-16 z^6 a^{-2} +34 z^6 a^{-4} +19 z^6 a^{-6} -5 z^6 a^{-8} -20 z^6+3 a^3 z^5-12 a z^5+12 z^5 a^{-1} +36 z^5 a^{-3} +30 z^5 a^{-5} +21 z^5 a^{-7} +a^4 z^4-6 a^2 z^4+20 z^4 a^{-2} -17 z^4 a^{-4} -9 z^4 a^{-6} +8 z^4 a^{-8} +13 z^4-2 a^3 z^3+7 a z^3-6 z^3 a^{-1} -16 z^3 a^{-3} -12 z^3 a^{-5} -11 z^3 a^{-7} -a^4 z^2+4 a^2 z^2-11 z^2 a^{-2} +5 z^2 a^{-4} +5 z^2 a^{-6} -4 z^2 a^{-8} -2 z^2+2 z a^{-1} +2 z a^{-3} +2 z a^{-5} +2 z a^{-7} -a^2+2 a^{-2} - a^{-6} +1 }[/math] |
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