K13a836
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Polynomial invariants
| Jones polynomial | Data:K13a836/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -t^5+5 t^4-12 t^3+20 t^2-28 t+33-28 t^{-1} +20 t^{-2} -12 t^{-3} +5 t^{-4} - t^{-5} }[/math] |
| Conway polynomial | Data:K13a836/Conway Polynomial |
| Determinant | 165 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^{10}+2 a^2 z^8+z^8 a^{-2} -8 z^8-a^4 z^6+13 a^2 z^6+6 z^6 a^{-2} -25 z^6-5 a^4 z^4+29 a^2 z^4+12 z^4 a^{-2} -38 z^4-7 a^4 z^2+25 a^2 z^2+9 z^2 a^{-2} -28 z^2-2 a^4+7 a^2+3 a^{-2} -7 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^2 z^{12}+z^{12}+3 a^3 z^{11}+7 a z^{11}+4 z^{11} a^{-1} +4 a^4 z^{10}+5 a^2 z^{10}+6 z^{10} a^{-2} +7 z^{10}+4 a^5 z^9-8 a^3 z^9-30 a z^9-12 z^9 a^{-1} +6 z^9 a^{-3} +3 a^6 z^8-12 a^4 z^8-36 a^2 z^8-21 z^8 a^{-2} +5 z^8 a^{-4} -47 z^8+a^7 z^7-13 a^5 z^7+8 a^3 z^7+56 a z^7+13 z^7 a^{-1} -18 z^7 a^{-3} +3 z^7 a^{-5} -12 a^6 z^6+10 a^4 z^6+86 a^2 z^6+30 z^6 a^{-2} -15 z^6 a^{-4} +z^6 a^{-6} +110 z^6-4 a^7 z^5+8 a^5 z^5-7 a^3 z^5-40 a z^5+3 z^5 a^{-1} +15 z^5 a^{-3} -9 z^5 a^{-5} +13 a^6 z^4-8 a^4 z^4-94 a^2 z^4-18 z^4 a^{-2} +11 z^4 a^{-4} -3 z^4 a^{-6} -105 z^4+4 a^7 z^3+2 a^5 z^3+a^3 z^3+6 a z^3-3 z^3 a^{-1} -z^3 a^{-3} +5 z^3 a^{-5} -4 a^6 z^2+7 a^4 z^2+42 a^2 z^2+9 z^2 a^{-2} -3 z^2 a^{-4} +z^2 a^{-6} +44 z^2-a^7 z-a^5 z+a^3 z+a z-z a^{-3} -z a^{-5} -2 a^4-7 a^2-3 a^{-2} -7 }[/math] |
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