K12a157
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+3 q^6-7 q^5+14 q^4-21 q^3+27 q^2-30 q+29-24 q^{-1} +18 q^{-2} -10 q^{-3} +4 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+22 t^2-40 t+49-40 t^{-1} +22 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6+z^2+1 }[/math] |
| Determinant | 189 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-a^2 z^6-3 z^6 a^{-2} +5 z^6-3 a^2 z^4-12 z^4 a^{-2} +3 z^4 a^{-4} +12 z^4-4 a^2 z^2-18 z^2 a^{-2} +9 z^2 a^{-4} -z^2 a^{-6} +15 z^2-2 a^2-10 a^{-2} +7 a^{-4} -2 a^{-6} +8 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +8 z^{10} a^{-2} +3 z^{10} a^{-4} +5 z^{10}+11 a z^9+19 z^9 a^{-1} +12 z^9 a^{-3} +4 z^9 a^{-5} +13 a^2 z^8+2 z^8 a^{-2} +3 z^8 a^{-4} +3 z^8 a^{-6} +15 z^8+9 a^3 z^7-9 a z^7-42 z^7 a^{-1} -34 z^7 a^{-3} -9 z^7 a^{-5} +z^7 a^{-7} +4 a^4 z^6-21 a^2 z^6-51 z^6 a^{-2} -31 z^6 a^{-4} -11 z^6 a^{-6} -56 z^6+a^5 z^5-12 a^3 z^5-9 a z^5+23 z^5 a^{-1} +24 z^5 a^{-3} +z^5 a^{-5} -4 z^5 a^{-7} -4 a^4 z^4+17 a^2 z^4+74 z^4 a^{-2} +46 z^4 a^{-4} +14 z^4 a^{-6} +63 z^4-a^5 z^3+7 a^3 z^3+13 a z^3-3 z^3 a^{-3} +7 z^3 a^{-5} +5 z^3 a^{-7} +a^4 z^2-9 a^2 z^2-46 z^2 a^{-2} -29 z^2 a^{-4} -8 z^2 a^{-6} -35 z^2-2 a^3 z-4 a z-2 z a^{-1} -z a^{-3} -3 z a^{-5} -2 z a^{-7} +2 a^2+10 a^{-2} +7 a^{-4} +2 a^{-6} +8 }[/math] |
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