K12a518
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+4 q^6-7 q^5+12 q^4-18 q^3+22 q^2-24 q+23-19 q^{-1} +14 q^{-2} -8 q^{-3} +4 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+13 t^2-37 t+53-37 t^{-1} +13 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+z^4-3 z^2+1 }[/math] |
| Determinant | 157 |
| 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} -z^4-a^4 z^2+2 a^2 z^2-5 z^2 a^{-2} +3 z^2 a^{-4} -z^2 a^{-6} -z^2+a^2-3 a^{-2} +2 a^{-4} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +8 z^{10} a^{-2} +4 z^{10} a^{-4} +4 z^{10}+7 a z^9+13 z^9 a^{-1} +12 z^9 a^{-3} +6 z^9 a^{-5} +8 a^2 z^8-14 z^8 a^{-2} -5 z^8 a^{-4} +4 z^8 a^{-6} +3 z^8+7 a^3 z^7-7 a z^7-44 z^7 a^{-1} -53 z^7 a^{-3} -22 z^7 a^{-5} +z^7 a^{-7} +4 a^4 z^6-9 a^2 z^6-11 z^6 a^{-2} -20 z^6 a^{-4} -15 z^6 a^{-6} -19 z^6+a^5 z^5-10 a^3 z^5+a z^5+57 z^5 a^{-1} +71 z^5 a^{-3} +23 z^5 a^{-5} -3 z^5 a^{-7} -6 a^4 z^4-a^2 z^4+38 z^4 a^{-2} +36 z^4 a^{-4} +14 z^4 a^{-6} +21 z^4-a^5 z^3+3 a^3 z^3-2 a z^3-34 z^3 a^{-1} -38 z^3 a^{-3} -9 z^3 a^{-5} +z^3 a^{-7} +2 a^4 z^2+3 a^2 z^2-24 z^2 a^{-2} -17 z^2 a^{-4} -3 z^2 a^{-6} -9 z^2+2 a z+8 z a^{-1} +7 z a^{-3} +z a^{-5} -a^2+3 a^{-2} +2 a^{-4} +1 }[/math] |
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