K13a1098
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-5 q^{11}+13 q^{10}-24 q^9+36 q^8-47 q^7+52 q^6-51 q^5+44 q^4-32 q^3+21 q^2-10 q+4-\frac{1}{q} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-13 t^3+40 t^2-72 t+87-72 t^{-1} +40 t^{-2} -13 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a1098/Conway Polynomial |
| Determinant | 341 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} +z^8 a^{-6} -z^6 a^{-2} +4 z^6 a^{-4} +2 z^6 a^{-6} -2 z^6 a^{-8} -3 z^4 a^{-2} +9 z^4 a^{-4} -z^4 a^{-6} -4 z^4 a^{-8} +z^4 a^{-10} -3 z^2 a^{-2} +12 z^2 a^{-4} -6 z^2 a^{-6} -z^2 a^{-8} +z^2 a^{-10} - a^{-2} +6 a^{-4} -5 a^{-6} + a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{12} a^{-6} +2 z^{12} a^{-8} +6 z^{11} a^{-5} +15 z^{11} a^{-7} +9 z^{11} a^{-9} +8 z^{10} a^{-4} +19 z^{10} a^{-6} +28 z^{10} a^{-8} +17 z^{10} a^{-10} +7 z^9 a^{-3} +3 z^9 a^{-5} -14 z^9 a^{-7} +8 z^9 a^{-9} +18 z^9 a^{-11} +4 z^8 a^{-2} -9 z^8 a^{-4} -48 z^8 a^{-6} -75 z^8 a^{-8} -28 z^8 a^{-10} +12 z^8 a^{-12} +z^7 a^{-1} -15 z^7 a^{-3} -26 z^7 a^{-5} -20 z^7 a^{-7} -51 z^7 a^{-9} -36 z^7 a^{-11} +5 z^7 a^{-13} -12 z^6 a^{-2} -15 z^6 a^{-4} +34 z^6 a^{-6} +74 z^6 a^{-8} +15 z^6 a^{-10} -21 z^6 a^{-12} +z^6 a^{-14} -3 z^5 a^{-1} +5 z^5 a^{-3} +14 z^5 a^{-5} +28 z^5 a^{-7} +55 z^5 a^{-9} +26 z^5 a^{-11} -7 z^5 a^{-13} +13 z^4 a^{-2} +27 z^4 a^{-4} -4 z^4 a^{-6} -32 z^4 a^{-8} -4 z^4 a^{-10} +9 z^4 a^{-12} -z^4 a^{-14} +3 z^3 a^{-1} +6 z^3 a^{-3} +6 z^3 a^{-5} -6 z^3 a^{-7} -19 z^3 a^{-9} -9 z^3 a^{-11} +z^3 a^{-13} -6 z^2 a^{-2} -18 z^2 a^{-4} -10 z^2 a^{-6} +5 z^2 a^{-8} +2 z^2 a^{-10} -z^2 a^{-12} -z a^{-1} -3 z a^{-3} -6 z a^{-5} -3 z a^{-7} +2 z a^{-9} +z a^{-11} + a^{-2} +6 a^{-4} +5 a^{-6} + a^{-8} }[/math] |
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