K13a4354
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Polynomial invariants
| Jones polynomial | Data:K13a4354/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ t^5-6 t^4+19 t^3-40 t^2+63 t-73+63 t^{-1} -40 t^{-2} +19 t^{-3} -6 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | Data:K13a4354/Conway Polynomial |
| Determinant | 331 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^{10} a^{-2} +7 z^8 a^{-2} -2 z^8 a^{-4} -z^8+21 z^6 a^{-2} -11 z^6 a^{-4} +z^6 a^{-6} -5 z^6+33 z^4 a^{-2} -23 z^4 a^{-4} +4 z^4 a^{-6} -10 z^4+27 z^2 a^{-2} -20 z^2 a^{-4} +5 z^2 a^{-6} -9 z^2+9 a^{-2} -6 a^{-4} + a^{-6} -3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{12} a^{-2} +3 z^{12} a^{-4} +10 z^{11} a^{-1} +19 z^{11} a^{-3} +9 z^{11} a^{-5} +20 z^{10} a^{-2} +20 z^{10} a^{-4} +13 z^{10} a^{-6} +13 z^{10}+9 a z^9-18 z^9 a^{-1} -42 z^9 a^{-3} -3 z^9 a^{-5} +12 z^9 a^{-7} +4 a^2 z^8-84 z^8 a^{-2} -69 z^8 a^{-4} -21 z^8 a^{-6} +8 z^8 a^{-8} -40 z^8+a^3 z^7-26 a z^7+2 z^7 a^{-1} +33 z^7 a^{-3} -20 z^7 a^{-5} -20 z^7 a^{-7} +4 z^7 a^{-9} -11 a^2 z^6+132 z^6 a^{-2} +98 z^6 a^{-4} +16 z^6 a^{-6} -13 z^6 a^{-8} +z^6 a^{-10} +53 z^6-3 a^3 z^5+25 a z^5+17 z^5 a^{-1} -2 z^5 a^{-3} +28 z^5 a^{-5} +11 z^5 a^{-7} -8 z^5 a^{-9} +7 a^2 z^4-112 z^4 a^{-2} -78 z^4 a^{-4} -10 z^4 a^{-6} +5 z^4 a^{-8} -2 z^4 a^{-10} -44 z^4+2 a^3 z^3-12 a z^3-22 z^3 a^{-1} -14 z^3 a^{-3} -11 z^3 a^{-5} +5 z^3 a^{-9} +47 z^2 a^{-2} +36 z^2 a^{-4} +6 z^2 a^{-6} +z^2 a^{-10} +18 z^2+3 a z+7 z a^{-1} +7 z a^{-3} +z a^{-5} -3 z a^{-7} -z a^{-9} -9 a^{-2} -6 a^{-4} - a^{-6} -3 }[/math] |
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