K13a785
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Polynomial invariants
| Jones polynomial | Data:K13a785/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-14 t^3+46 t^2-90 t+113-90 t^{-1} +46 t^{-2} -14 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a785/Conway Polynomial |
| Determinant | 417 |
| 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^4-4 a^2 z^4+5 z^4 a^{-2} -2 z^4 a^{-4} +2 z^4+a^4 z^2-4 a^2 z^2+4 z^2 a^{-2} -2 z^2 a^{-4} +z^2+a^4-2 a^2+2 a^{-2} - a^{-4} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{12} a^{-2} +3 z^{12}+12 a z^{11}+23 z^{11} a^{-1} +11 z^{11} a^{-3} +21 a^2 z^{10}+36 z^{10} a^{-2} +16 z^{10} a^{-4} +41 z^{10}+21 a^3 z^9+17 a z^9-14 z^9 a^{-1} +2 z^9 a^{-3} +12 z^9 a^{-5} +13 a^4 z^8-27 a^2 z^8-103 z^8 a^{-2} -34 z^8 a^{-4} +5 z^8 a^{-6} -104 z^8+5 a^5 z^7-39 a^3 z^7-90 a z^7-71 z^7 a^{-1} -55 z^7 a^{-3} -29 z^7 a^{-5} +z^7 a^{-7} +a^6 z^6-21 a^4 z^6-3 a^2 z^6+90 z^6 a^{-2} +23 z^6 a^{-4} -11 z^6 a^{-6} +75 z^6-6 a^5 z^5+31 a^3 z^5+101 a z^5+100 z^5 a^{-1} +62 z^5 a^{-3} +24 z^5 a^{-5} -2 z^5 a^{-7} -a^6 z^4+12 a^4 z^4+22 a^2 z^4-33 z^4 a^{-2} -11 z^4 a^{-4} +7 z^4 a^{-6} -6 z^4+a^5 z^3-15 a^3 z^3-43 a z^3-44 z^3 a^{-1} -28 z^3 a^{-3} -10 z^3 a^{-5} +z^3 a^{-7} -5 a^4 z^2-13 a^2 z^2+6 z^2 a^{-2} +4 z^2 a^{-4} -z^2 a^{-6} -7 z^2+3 a^3 z+7 a z+7 z a^{-1} +5 z a^{-3} +2 z a^{-5} +a^4+2 a^2-2 a^{-2} - a^{-4} +1 }[/math] |
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