K13a86
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Polynomial invariants
| Jones polynomial | Data:K13a86/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-11 t^3+25 t^2-32 t+33-32 t^{-1} +25 t^{-2} -11 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a86/Conway Polynomial |
| Determinant | 173 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} +z^8 a^{-6} -2 z^6 a^{-2} +3 z^6 a^{-4} +5 z^6 a^{-6} -z^6 a^{-8} -7 z^4 a^{-2} -z^4 a^{-4} +10 z^4 a^{-6} -4 z^4 a^{-8} +z^4-4 z^2 a^{-2} -6 z^2 a^{-4} +12 z^2 a^{-6} -4 z^2 a^{-8} +3 z^2+ a^{-2} -4 a^{-4} +5 a^{-6} -2 a^{-8} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{12} a^{-4} +z^{12} a^{-6} +3 z^{11} a^{-3} +7 z^{11} a^{-5} +4 z^{11} a^{-7} +4 z^{10} a^{-2} +6 z^{10} a^{-4} +8 z^{10} a^{-6} +6 z^{10} a^{-8} +3 z^9 a^{-1} -6 z^9 a^{-3} -24 z^9 a^{-5} -9 z^9 a^{-7} +6 z^9 a^{-9} -15 z^8 a^{-2} -36 z^8 a^{-4} -42 z^8 a^{-6} -16 z^8 a^{-8} +6 z^8 a^{-10} +z^8-14 z^7 a^{-1} -10 z^7 a^{-3} +30 z^7 a^{-5} +11 z^7 a^{-7} -10 z^7 a^{-9} +5 z^7 a^{-11} +12 z^6 a^{-2} +57 z^6 a^{-4} +79 z^6 a^{-6} +25 z^6 a^{-8} -11 z^6 a^{-10} +3 z^6 a^{-12} -5 z^6+20 z^5 a^{-1} +20 z^5 a^{-3} -24 z^5 a^{-5} -9 z^5 a^{-7} +4 z^5 a^{-9} -10 z^5 a^{-11} +z^5 a^{-13} +2 z^4 a^{-2} -50 z^4 a^{-4} -78 z^4 a^{-6} -20 z^4 a^{-8} +8 z^4 a^{-10} -6 z^4 a^{-12} +8 z^4-10 z^3 a^{-1} -7 z^3 a^{-3} +8 z^3 a^{-5} +4 z^3 a^{-7} +8 z^3 a^{-9} +7 z^3 a^{-11} -2 z^3 a^{-13} -z^2 a^{-2} +25 z^2 a^{-4} +33 z^2 a^{-6} +10 z^2 a^{-8} +2 z^2 a^{-12} -5 z^2+z a^{-1} +z a^{-3} -z a^{-5} -2 z a^{-7} -3 z a^{-9} -2 z a^{-11} - a^{-2} -4 a^{-4} -5 a^{-6} -2 a^{-8} +1 }[/math] |
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