K13a2153
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Polynomial invariants
| Jones polynomial | Data:K13a2153/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-11 t^3+35 t^2-68 t+85-68 t^{-1} +35 t^{-2} -11 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a2153/Conway Polynomial |
| Determinant | 317 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-2} +z^8-a^2 z^6+4 z^6 a^{-2} -2 z^6 a^{-4} +4 z^6-3 a^2 z^4+10 z^4 a^{-2} -6 z^4 a^{-4} +z^4 a^{-6} +7 z^4-4 a^2 z^2+13 z^2 a^{-2} -8 z^2 a^{-4} +z^2 a^{-6} +3 z^2-a^2+7 a^{-2} -4 a^{-4} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{12} a^{-2} +2 z^{12} a^{-4} +8 z^{11} a^{-1} +15 z^{11} a^{-3} +7 z^{11} a^{-5} +27 z^{10} a^{-2} +20 z^{10} a^{-4} +9 z^{10} a^{-6} +16 z^{10}+20 a z^9+16 z^9 a^{-1} -19 z^9 a^{-3} -10 z^9 a^{-5} +5 z^9 a^{-7} +17 a^2 z^8-81 z^8 a^{-2} -84 z^8 a^{-4} -33 z^8 a^{-6} +z^8 a^{-8} -14 z^8+10 a^3 z^7-32 a z^7-78 z^7 a^{-1} -45 z^7 a^{-3} -28 z^7 a^{-5} -19 z^7 a^{-7} +4 a^4 z^6-27 a^2 z^6+74 z^6 a^{-2} +101 z^6 a^{-4} +38 z^6 a^{-6} -3 z^6 a^{-8} -17 z^6+a^5 z^5-12 a^3 z^5+21 a z^5+84 z^5 a^{-1} +85 z^5 a^{-3} +57 z^5 a^{-5} +22 z^5 a^{-7} -3 a^4 z^4+23 a^2 z^4-46 z^4 a^{-2} -57 z^4 a^{-4} -15 z^4 a^{-6} +2 z^4 a^{-8} +20 z^4-a^5 z^3+8 a^3 z^3-5 a z^3-47 z^3 a^{-1} -55 z^3 a^{-3} -28 z^3 a^{-5} -6 z^3 a^{-7} -8 a^2 z^2+23 z^2 a^{-2} +22 z^2 a^{-4} +3 z^2 a^{-6} -4 z^2-2 a^3 z+a z+11 z a^{-1} +14 z a^{-3} +4 z a^{-5} -2 z a^{-7} +a^2-7 a^{-2} -4 a^{-4} -1 }[/math] |
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