K13a1068
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Polynomial invariants
| Jones polynomial | Data:K13a1068/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-13 t^3+45 t^2-91 t+115-91 t^{-1} +45 t^{-2} -13 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a1068/Conway Polynomial |
| Determinant | 417 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^8+z^8-a^4 z^6+4 a^2 z^6-2 z^6 a^{-2} +2 z^6-3 a^4 z^4+10 a^2 z^4-3 z^4 a^{-2} +z^4 a^{-4} +2 z^4-5 a^4 z^2+11 a^2 z^2-2 z^2 a^{-2} -3 a^4+5 a^2- a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^2 z^{12}+3 z^{12}+9 a^3 z^{11}+22 a z^{11}+13 z^{11} a^{-1} +12 a^4 z^{10}+29 a^2 z^{10}+24 z^{10} a^{-2} +41 z^{10}+9 a^5 z^9+3 a^3 z^9-14 a z^9+17 z^9 a^{-1} +25 z^9 a^{-3} +4 a^6 z^8-23 a^4 z^8-79 a^2 z^8-28 z^8 a^{-2} +16 z^8 a^{-4} -96 z^8+a^7 z^7-22 a^5 z^7-46 a^3 z^7-56 a z^7-79 z^7 a^{-1} -40 z^7 a^{-3} +6 z^7 a^{-5} -10 a^6 z^6+15 a^4 z^6+70 a^2 z^6-8 z^6 a^{-2} -22 z^6 a^{-4} +z^6 a^{-6} +60 z^6-3 a^7 z^5+21 a^5 z^5+61 a^3 z^5+77 a z^5+60 z^5 a^{-1} +15 z^5 a^{-3} -5 z^5 a^{-5} +8 a^6 z^4-9 a^4 z^4-31 a^2 z^4+15 z^4 a^{-2} +6 z^4 a^{-4} -5 z^4+3 a^7 z^3-12 a^5 z^3-38 a^3 z^3-34 a z^3-9 z^3 a^{-1} +2 z^3 a^{-3} -2 a^6 z^2+7 a^4 z^2+12 a^2 z^2-5 z^2 a^{-2} -2 z^2-a^7 z+4 a^5 z+10 a^3 z+6 a z-z a^{-1} -2 z a^{-3} -3 a^4-5 a^2+ a^{-2} }[/math] |
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