K12a62
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+3 q^6-6 q^5+11 q^4-15 q^3+18 q^2-20 q+19-15 q^{-1} +11 q^{-2} -6 q^{-3} +3 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+12 t^2-30 t+41-30 t^{-1} +12 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 1-2 z^6 }[/math] |
| Determinant | 129 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-2} -z^6+2 a^2 z^4-2 z^4 a^{-2} +2 z^4 a^{-4} -2 z^4-a^4 z^2+4 a^2 z^2-3 z^2 a^{-2} +4 z^2 a^{-4} -z^2 a^{-6} -3 z^2-a^4+3 a^2-2 a^{-2} +3 a^{-4} - a^{-6} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +6 z^{10} a^{-2} +3 z^{10} a^{-4} +3 z^{10}+4 a z^9+6 z^9 a^{-1} +6 z^9 a^{-3} +4 z^9 a^{-5} +4 a^2 z^8-13 z^8 a^{-2} -4 z^8 a^{-4} +3 z^8 a^{-6} -2 z^8+4 a^3 z^7-3 a z^7-22 z^7 a^{-1} -29 z^7 a^{-3} -13 z^7 a^{-5} +z^7 a^{-7} +3 a^4 z^6-15 z^6 a^{-4} -12 z^6 a^{-6} +a^5 z^5-4 a^3 z^5+2 a z^5+30 z^5 a^{-1} +36 z^5 a^{-3} +9 z^5 a^{-5} -4 z^5 a^{-7} -6 a^4 z^4-10 a^2 z^4+19 z^4 a^{-2} +29 z^4 a^{-4} +14 z^4 a^{-6} -2 a^5 z^3-2 a^3 z^3-5 a z^3-19 z^3 a^{-1} -19 z^3 a^{-3} -z^3 a^{-5} +4 z^3 a^{-7} +4 a^4 z^2+9 a^2 z^2-14 z^2 a^{-2} -18 z^2 a^{-4} -7 z^2 a^{-6} +2 z^2+a^5 z+2 a^3 z+3 a z+6 z a^{-1} +5 z a^{-3} -z a^{-7} -a^4-3 a^2+2 a^{-2} +3 a^{-4} + a^{-6} -1 }[/math] |
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