K13a3309
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Polynomial invariants
| Jones polynomial | Data:K13a3309/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ t^5-5 t^4+14 t^3-25 t^2+35 t-39+35 t^{-1} -25 t^{-2} +14 t^{-3} -5 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | Data:K13a3309/Conway Polynomial |
| Determinant | 199 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^{10} a^{-6} -z^8 a^{-4} +8 z^8 a^{-6} -2 z^8 a^{-8} -6 z^6 a^{-4} +26 z^6 a^{-6} -12 z^6 a^{-8} +z^6 a^{-10} -12 z^4 a^{-4} +43 z^4 a^{-6} -26 z^4 a^{-8} +4 z^4 a^{-10} -9 z^2 a^{-4} +35 z^2 a^{-6} -25 z^2 a^{-8} +5 z^2 a^{-10} -2 a^{-4} +10 a^{-6} -9 a^{-8} +2 a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{12} a^{-6} +z^{12} a^{-8} +3 z^{11} a^{-5} +8 z^{11} a^{-7} +5 z^{11} a^{-9} +3 z^{10} a^{-4} +7 z^{10} a^{-6} +15 z^{10} a^{-8} +11 z^{10} a^{-10} +z^9 a^{-3} -12 z^9 a^{-5} -26 z^9 a^{-7} +3 z^9 a^{-9} +16 z^9 a^{-11} -18 z^8 a^{-4} -56 z^8 a^{-6} -73 z^8 a^{-8} -17 z^8 a^{-10} +18 z^8 a^{-12} -6 z^7 a^{-3} +6 z^7 a^{-5} +6 z^7 a^{-7} -49 z^7 a^{-9} -28 z^7 a^{-11} +15 z^7 a^{-13} +38 z^6 a^{-4} +118 z^6 a^{-6} +111 z^6 a^{-8} -9 z^6 a^{-10} -31 z^6 a^{-12} +9 z^6 a^{-14} +12 z^5 a^{-3} +23 z^5 a^{-5} +46 z^5 a^{-7} +62 z^5 a^{-9} +3 z^5 a^{-11} -20 z^5 a^{-13} +4 z^5 a^{-15} -35 z^4 a^{-4} -108 z^4 a^{-6} -86 z^4 a^{-8} +8 z^4 a^{-10} +14 z^4 a^{-12} -6 z^4 a^{-14} +z^4 a^{-16} -9 z^3 a^{-3} -26 z^3 a^{-5} -47 z^3 a^{-7} -33 z^3 a^{-9} +7 z^3 a^{-11} +9 z^3 a^{-13} -z^3 a^{-15} +15 z^2 a^{-4} +50 z^2 a^{-6} +40 z^2 a^{-8} +3 z^2 a^{-10} -z^2 a^{-12} +z^2 a^{-14} +2 z a^{-3} +7 z a^{-5} +14 z a^{-7} +8 z a^{-9} -2 z a^{-11} -z a^{-13} -2 a^{-4} -10 a^{-6} -9 a^{-8} -2 a^{-10} }[/math] |
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