K13a3642
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Polynomial invariants
| Jones polynomial | Data:K13a3642/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ t^5-7 t^4+25 t^3-56 t^2+89 t-103+89 t^{-1} -56 t^{-2} +25 t^{-3} -7 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | Data:K13a3642/Conway Polynomial |
| Determinant | 459 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^{10} a^{-2} +6 z^8 a^{-2} -2 z^8 a^{-4} -z^8+16 z^6 a^{-2} -9 z^6 a^{-4} +z^6 a^{-6} -4 z^6+23 z^4 a^{-2} -15 z^4 a^{-4} +3 z^4 a^{-6} -7 z^4+16 z^2 a^{-2} -9 z^2 a^{-4} +2 z^2 a^{-6} -6 z^2+3 a^{-2} - a^{-6} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 5 z^{12} a^{-2} +5 z^{12} a^{-4} +16 z^{11} a^{-1} +33 z^{11} a^{-3} +17 z^{11} a^{-5} +40 z^{10} a^{-2} +44 z^{10} a^{-4} +24 z^{10} a^{-6} +20 z^{10}+13 a z^9-12 z^9 a^{-1} -48 z^9 a^{-3} -3 z^9 a^{-5} +20 z^9 a^{-7} +5 a^2 z^8-132 z^8 a^{-2} -132 z^8 a^{-4} -38 z^8 a^{-6} +12 z^8 a^{-8} -45 z^8+a^3 z^7-29 a z^7-38 z^7 a^{-1} -18 z^7 a^{-3} -45 z^7 a^{-5} -30 z^7 a^{-7} +5 z^7 a^{-9} -10 a^2 z^6+144 z^6 a^{-2} +137 z^6 a^{-4} +24 z^6 a^{-6} -17 z^6 a^{-8} +z^6 a^{-10} +39 z^6-2 a^3 z^5+24 a z^5+51 z^5 a^{-1} +52 z^5 a^{-3} +48 z^5 a^{-5} +14 z^5 a^{-7} -7 z^5 a^{-9} +6 a^2 z^4-86 z^4 a^{-2} -69 z^4 a^{-4} -5 z^4 a^{-6} +8 z^4 a^{-8} -z^4 a^{-10} -25 z^4+a^3 z^3-11 a z^3-26 z^3 a^{-1} -25 z^3 a^{-3} -11 z^3 a^{-5} +3 z^3 a^{-7} +3 z^3 a^{-9} -a^2 z^2+27 z^2 a^{-2} +15 z^2 a^{-4} -2 z^2 a^{-6} -z^2 a^{-8} +10 z^2+2 a z+5 z a^{-1} +4 z a^{-3} -2 z a^{-5} -3 z a^{-7} -3 a^{-2} + a^{-6} -1 }[/math] |
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