K12a250
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{10}-4 q^9+8 q^8-14 q^7+20 q^6-23 q^5+24 q^4-22 q^3+18 q^2-12 q+7-3 q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+20 t^2-32 t+37-32 t^{-1} +20 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6-2 z^4+z^2+1 }[/math] |
| Determinant | 157 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} -2 z^6 a^{-2} +5 z^6 a^{-4} -2 z^6 a^{-6} -8 z^4 a^{-2} +11 z^4 a^{-4} -7 z^4 a^{-6} +z^4 a^{-8} +z^4-10 z^2 a^{-2} +13 z^2 a^{-4} -7 z^2 a^{-6} +2 z^2 a^{-8} +3 z^2-4 a^{-2} +5 a^{-4} -2 a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +3 z^{10} a^{-2} +8 z^{10} a^{-4} +5 z^{10} a^{-6} +3 z^9 a^{-1} +9 z^9 a^{-3} +17 z^9 a^{-5} +11 z^9 a^{-7} -7 z^8 a^{-2} -13 z^8 a^{-4} +9 z^8 a^{-6} +14 z^8 a^{-8} +z^8-14 z^7 a^{-1} -47 z^7 a^{-3} -59 z^7 a^{-5} -14 z^7 a^{-7} +12 z^7 a^{-9} -9 z^6 a^{-2} -30 z^6 a^{-4} -57 z^6 a^{-6} -23 z^6 a^{-8} +8 z^6 a^{-10} -5 z^6+22 z^5 a^{-1} +62 z^5 a^{-3} +49 z^5 a^{-5} -9 z^5 a^{-7} -14 z^5 a^{-9} +4 z^5 a^{-11} +32 z^4 a^{-2} +62 z^4 a^{-4} +57 z^4 a^{-6} +11 z^4 a^{-8} -6 z^4 a^{-10} +z^4 a^{-12} +9 z^4-13 z^3 a^{-1} -27 z^3 a^{-3} -9 z^3 a^{-5} +11 z^3 a^{-7} +4 z^3 a^{-9} -2 z^3 a^{-11} -23 z^2 a^{-2} -32 z^2 a^{-4} -19 z^2 a^{-6} -2 z^2 a^{-8} +z^2 a^{-10} -7 z^2+2 z a^{-1} +3 z a^{-3} -z a^{-5} -2 z a^{-7} +4 a^{-2} +5 a^{-4} +2 a^{-6} +2 }[/math] |
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