K12a180
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+3 q^6-7 q^5+13 q^4-19 q^3+25 q^2-27 q+26-22 q^{-1} +16 q^{-2} -9 q^{-3} +4 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+15 t^2-41 t+57-41 t^{-1} +15 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+3 z^4+z^2+1 }[/math] |
| Determinant | 173 |
| 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} -a^4 z^2+a^2 z^2-2 z^2 a^{-2} +3 z^2 a^{-4} -z^2 a^{-6} +z^2- a^{-2} +2 a^{-4} - a^{-6} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +7 z^{10} a^{-2} +3 z^{10} a^{-4} +4 z^{10}+8 a z^9+13 z^9 a^{-1} +9 z^9 a^{-3} +4 z^9 a^{-5} +10 a^2 z^8-3 z^8 a^{-2} +3 z^8 a^{-6} +10 z^8+8 a^3 z^7-2 a z^7-24 z^7 a^{-1} -25 z^7 a^{-3} -10 z^7 a^{-5} +z^7 a^{-7} +4 a^4 z^6-12 a^2 z^6-21 z^6 a^{-2} -19 z^6 a^{-4} -11 z^6 a^{-6} -29 z^6+a^5 z^5-11 a^3 z^5-13 a z^5+6 z^5 a^{-1} +14 z^5 a^{-3} +3 z^5 a^{-5} -4 z^5 a^{-7} -5 a^4 z^4+4 a^2 z^4+22 z^4 a^{-2} +24 z^4 a^{-4} +13 z^4 a^{-6} +20 z^4-a^5 z^3+6 a^3 z^3+11 a z^3+5 z^3 a^{-1} +2 z^3 a^{-3} +6 z^3 a^{-5} +5 z^3 a^{-7} +2 a^4 z^2-8 z^2 a^{-2} -10 z^2 a^{-4} -6 z^2 a^{-6} -6 z^2-a^3 z-3 a z-3 z a^{-1} -2 z a^{-3} -3 z a^{-5} -2 z a^{-7} + a^{-2} +2 a^{-4} + a^{-6} +1 }[/math] |
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