K13a2531
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Polynomial invariants
| Jones polynomial | Data:K13a2531/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-14 t^3+41 t^2-75 t+93-75 t^{-1} +41 t^{-2} -14 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a2531/Conway Polynomial |
| Determinant | 357 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-2} +z^8-2 a^2 z^6+3 z^6 a^{-2} -z^6 a^{-4} +2 z^6+a^4 z^4-5 a^2 z^4+3 z^4 a^{-2} -2 z^4 a^{-4} +2 a^4 z^2-5 a^2 z^2-2 z^2+2 a^4-2 a^2+ a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{12} a^{-2} +3 z^{12}+10 a z^{11}+20 z^{11} a^{-1} +10 z^{11} a^{-3} +15 a^2 z^{10}+24 z^{10} a^{-2} +14 z^{10} a^{-4} +25 z^{10}+15 a^3 z^9-35 z^9 a^{-1} -9 z^9 a^{-3} +11 z^9 a^{-5} +10 a^4 z^8-19 a^2 z^8-86 z^8 a^{-2} -36 z^8 a^{-4} +5 z^8 a^{-6} -74 z^8+4 a^5 z^7-27 a^3 z^7-25 a z^7+10 z^7 a^{-1} -28 z^7 a^{-3} -31 z^7 a^{-5} +z^7 a^{-7} +a^6 z^6-19 a^4 z^6+103 z^6 a^{-2} +27 z^6 a^{-4} -13 z^6 a^{-6} +83 z^6-6 a^5 z^5+21 a^3 z^5+20 a z^5+10 z^5 a^{-1} +44 z^5 a^{-3} +25 z^5 a^{-5} -2 z^5 a^{-7} -2 a^6 z^4+17 a^4 z^4+12 a^2 z^4-54 z^4 a^{-2} -5 z^4 a^{-4} +7 z^4 a^{-6} -49 z^4+2 a^5 z^3-10 a^3 z^3-2 a z^3-z^3 a^{-1} -17 z^3 a^{-3} -6 z^3 a^{-5} +a^6 z^2-10 a^4 z^2-9 a^2 z^2+9 z^2 a^{-2} -2 z^2 a^{-4} +13 z^2+2 a^3 z-a z-3 z a^{-1} +2 a^4+2 a^2+ a^{-4} }[/math] |
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