K12a640
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^8-4 q^7+7 q^6-11 q^5+15 q^4-17 q^3+19 q^2-17 q+14-10 q^{-1} +6 q^{-2} -3 q^{-3} + q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+14 t^2-28 t+35-28 t^{-1} +14 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^6-4 z^4+z^2+1 }[/math] |
| Determinant | 125 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-2} -z^6 a^{-4} -z^6+a^2 z^4-z^4 a^{-2} -2 z^4 a^{-4} +z^4 a^{-6} -3 z^4+2 a^2 z^2+2 z^2 a^{-2} +z^2 a^{-6} -4 z^2+a^2+2 a^{-2} + a^{-4} - a^{-6} -2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +5 z^{10} a^{-2} +10 z^{10} a^{-4} +5 z^{10} a^{-6} +6 z^9 a^{-1} +3 z^9 a^{-3} +z^9 a^{-5} +4 z^9 a^{-7} -11 z^8 a^{-2} -40 z^8 a^{-4} -22 z^8 a^{-6} +z^8 a^{-8} +6 z^8+6 a z^7-9 z^7 a^{-1} -29 z^7 a^{-3} -33 z^7 a^{-5} -19 z^7 a^{-7} +5 a^2 z^6+7 z^6 a^{-2} +46 z^6 a^{-4} +26 z^6 a^{-6} -4 z^6 a^{-8} -4 z^6+3 a^3 z^5-5 a z^5+35 z^5 a^{-3} +53 z^5 a^{-5} +26 z^5 a^{-7} +a^4 z^4-5 a^2 z^4-10 z^4 a^{-2} -19 z^4 a^{-4} -7 z^4 a^{-6} +4 z^4 a^{-8} -8 z^4-3 a^3 z^3-14 z^3 a^{-3} -21 z^3 a^{-5} -10 z^3 a^{-7} -a^4 z^2+3 a^2 z^2+7 z^2 a^{-2} +3 z^2 a^{-4} -z^2 a^{-6} -z^2 a^{-8} +8 z^2+a^3 z+a z+z a^{-3} -z a^{-7} -a^2-2 a^{-2} + a^{-4} + a^{-6} -2 }[/math] |
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