K12a781
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+4 q^6-8 q^5+13 q^4-19 q^3+23 q^2-24 q+23-18 q^{-1} +13 q^{-2} -7 q^{-3} +3 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+14 t^2-37 t+51-37 t^{-1} +14 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+2 z^4+z^2+1 }[/math] |
| Determinant | 157 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-2} -z^6+2 a^2 z^4-z^4 a^{-2} +2 z^4 a^{-4} -z^4-a^4 z^2+3 a^2 z^2-z^2 a^{-2} +2 z^2 a^{-4} -z^2 a^{-6} -z^2-a^4+2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-1} +2 z^{11} a^{-3} +11 z^{10} a^{-2} +6 z^{10} a^{-4} +5 z^{10}+6 a z^9+6 z^9 a^{-1} +7 z^9 a^{-3} +7 z^9 a^{-5} +6 a^2 z^8-34 z^8 a^{-2} -17 z^8 a^{-4} +4 z^8 a^{-6} -7 z^8+5 a^3 z^7-6 a z^7-28 z^7 a^{-1} -44 z^7 a^{-3} -26 z^7 a^{-5} +z^7 a^{-7} +3 a^4 z^6-5 a^2 z^6+37 z^6 a^{-2} +7 z^6 a^{-4} -14 z^6 a^{-6} +8 z^6+a^5 z^5-6 a^3 z^5+2 a z^5+39 z^5 a^{-1} +60 z^5 a^{-3} +27 z^5 a^{-5} -3 z^5 a^{-7} -5 a^4 z^4-3 a^2 z^4-16 z^4 a^{-2} +6 z^4 a^{-4} +11 z^4 a^{-6} -9 z^4-2 a^5 z^3+a^3 z^3-2 a z^3-22 z^3 a^{-1} -28 z^3 a^{-3} -10 z^3 a^{-5} +z^3 a^{-7} +3 a^4 z^2+5 a^2 z^2+2 z^2 a^{-2} -2 z^2 a^{-4} -2 z^2 a^{-6} +4 z^2+a^5 z+a^3 z+a z+3 z a^{-1} +3 z a^{-3} +z a^{-5} -a^4-2 a^2 }[/math] |
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