K12a495
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{11}+5 q^{10}-12 q^9+21 q^8-31 q^7+37 q^6-39 q^5+36 q^4-28 q^3+20 q^2-10 q+4- q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-11 t^3+30 t^2-50 t+59-50 t^{-1} +30 t^{-2} -11 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+5 z^6+4 z^4+3 z^2+1 }[/math] |
| Determinant | 245 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} +z^8 a^{-6} -z^6 a^{-2} +4 z^6 a^{-4} +3 z^6 a^{-6} -z^6 a^{-8} -3 z^4 a^{-2} +8 z^4 a^{-4} +z^4 a^{-6} -2 z^4 a^{-8} -3 z^2 a^{-2} +11 z^2 a^{-4} -5 z^2 a^{-6} - a^{-2} +6 a^{-4} -5 a^{-6} + a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-5} +3 z^{11} a^{-7} +7 z^{10} a^{-4} +18 z^{10} a^{-6} +11 z^{10} a^{-8} +7 z^9 a^{-3} +14 z^9 a^{-5} +25 z^9 a^{-7} +18 z^9 a^{-9} +4 z^8 a^{-2} -7 z^8 a^{-4} -26 z^8 a^{-6} +3 z^8 a^{-8} +18 z^8 a^{-10} +z^7 a^{-1} -16 z^7 a^{-3} -46 z^7 a^{-5} -62 z^7 a^{-7} -21 z^7 a^{-9} +12 z^7 a^{-11} -12 z^6 a^{-2} -18 z^6 a^{-4} -13 z^6 a^{-6} -36 z^6 a^{-8} -24 z^6 a^{-10} +5 z^6 a^{-12} -3 z^5 a^{-1} +7 z^5 a^{-3} +28 z^5 a^{-5} +32 z^5 a^{-7} -13 z^5 a^{-11} +z^5 a^{-13} +13 z^4 a^{-2} +29 z^4 a^{-4} +28 z^4 a^{-6} +25 z^4 a^{-8} +10 z^4 a^{-10} -3 z^4 a^{-12} +3 z^3 a^{-1} +5 z^3 a^{-3} +5 z^3 a^{-5} +5 z^3 a^{-7} +6 z^3 a^{-9} +4 z^3 a^{-11} -6 z^2 a^{-2} -18 z^2 a^{-4} -15 z^2 a^{-6} -4 z^2 a^{-8} -z^2 a^{-10} -z a^{-1} -3 z a^{-3} -7 z a^{-5} -6 z a^{-7} -z a^{-9} + a^{-2} +6 a^{-4} +5 a^{-6} + a^{-8} }[/math] |
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