K13n157
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Polynomial invariants
| Jones polynomial | Data:K13n157/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-12 t^2+31 t-41+31 t^{-1} -12 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | Data:K13n157/Conway Polynomial |
| Determinant | 131 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6 a^{-4} +z^4 a^{-2} +2 z^4 a^{-4} -z^4 a^{-6} -2 z^4+a^2 z^2+3 z^2 a^{-4} -3 z^2+a^2+ a^{-4} + a^{-6} - a^{-8} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +3 z^{10} a^{-2} +6 z^{10} a^{-4} +3 z^{10} a^{-6} +4 z^9 a^{-1} +6 z^9 a^{-3} +5 z^9 a^{-5} +3 z^9 a^{-7} -2 z^8 a^{-2} -14 z^8 a^{-4} -7 z^8 a^{-6} +z^8 a^{-8} +4 z^8+3 a z^7-4 z^7 a^{-1} -21 z^7 a^{-3} -22 z^7 a^{-5} -8 z^7 a^{-7} +a^2 z^6-z^6 a^{-2} +13 z^6 a^{-4} +9 z^6 a^{-6} +2 z^6 a^{-8} -6 z^6-8 a z^5-4 z^5 a^{-1} +32 z^5 a^{-3} +38 z^5 a^{-5} +13 z^5 a^{-7} +3 z^5 a^{-9} -3 a^2 z^4-2 z^4 a^{-2} +5 z^4 a^{-4} -4 z^4 a^{-6} -10 z^4 a^{-8} -4 z^4+6 a z^3-22 z^3 a^{-3} -22 z^3 a^{-5} -14 z^3 a^{-7} -8 z^3 a^{-9} +3 a^2 z^2-z^2 a^{-2} -7 z^2 a^{-4} +3 z^2 a^{-6} +6 z^2 a^{-8} +6 z^2-a z+z a^{-1} +5 z a^{-3} +5 z a^{-5} +5 z a^{-7} +3 z a^{-9} -a^2+ a^{-4} - a^{-6} - a^{-8} -1 }[/math] |
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