K13a1057
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Polynomial invariants
| Jones polynomial | Data:K13a1057/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-12 t^3+31 t^2-50 t+59-50 t^{-1} +31 t^{-2} -12 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a1057/Conway Polynomial |
| Determinant | 249 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^8+z^8-2 a^4 z^6+3 a^2 z^6-z^6 a^{-2} +4 z^6+a^6 z^4-7 a^4 z^4+2 a^2 z^4-3 z^4 a^{-2} +6 z^4+3 a^6 z^2-8 a^4 z^2+a^2 z^2-2 z^2 a^{-2} +4 z^2+2 a^6-4 a^4+2 a^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^4 z^{12}+2 a^2 z^{12}+5 a^5 z^{11}+12 a^3 z^{11}+7 a z^{11}+5 a^6 z^{10}+6 a^4 z^{10}+13 a^2 z^{10}+12 z^{10}+3 a^7 z^9-15 a^5 z^9-36 a^3 z^9-4 a z^9+14 z^9 a^{-1} +a^8 z^8-19 a^6 z^8-39 a^4 z^8-51 a^2 z^8+12 z^8 a^{-2} -20 z^8-13 a^7 z^7+14 a^5 z^7+44 a^3 z^7-16 a z^7-25 z^7 a^{-1} +8 z^7 a^{-3} -5 a^8 z^6+23 a^6 z^6+61 a^4 z^6+64 a^2 z^6-18 z^6 a^{-2} +4 z^6 a^{-4} +9 z^6+18 a^7 z^5-12 a^5 z^5-43 a^3 z^5+16 a z^5+18 z^5 a^{-1} -10 z^5 a^{-3} +z^5 a^{-5} +8 a^8 z^4-13 a^6 z^4-55 a^4 z^4-45 a^2 z^4+10 z^4 a^{-2} -5 z^4 a^{-4} +4 z^4-9 a^7 z^3+8 a^5 z^3+22 a^3 z^3-a z^3-2 z^3 a^{-1} +3 z^3 a^{-3} -z^3 a^{-5} -4 a^8 z^2+7 a^6 z^2+25 a^4 z^2+14 a^2 z^2-z^2 a^{-2} +z^2 a^{-4} -2 z^2+2 a^7 z-4 a^3 z-2 a z-2 a^6-4 a^4-2 a^2+1 }[/math] |
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