K13a1080
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Polynomial invariants
| Jones polynomial | Data:K13a1080/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ t^5-6 t^4+21 t^3-47 t^2+75 t-87+75 t^{-1} -47 t^{-2} +21 t^{-3} -6 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | Data:K13a1080/Conway Polynomial |
| Determinant | 387 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^{10} a^{-2} +7 z^8 a^{-2} -2 z^8 a^{-4} -z^8+22 z^6 a^{-2} -10 z^6 a^{-4} +z^6 a^{-6} -5 z^6+37 z^4 a^{-2} -20 z^4 a^{-4} +3 z^4 a^{-6} -11 z^4+33 z^2 a^{-2} -19 z^2 a^{-4} +3 z^2 a^{-6} -12 z^2+13 a^{-2} -8 a^{-4} + a^{-6} -5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{12} a^{-2} +3 z^{12} a^{-4} +10 z^{11} a^{-1} +22 z^{11} a^{-3} +12 z^{11} a^{-5} +30 z^{10} a^{-2} +37 z^{10} a^{-4} +20 z^{10} a^{-6} +13 z^{10}+9 a z^9-5 z^9 a^{-1} -26 z^9 a^{-3} +7 z^9 a^{-5} +19 z^9 a^{-7} +4 a^2 z^8-104 z^8 a^{-2} -113 z^8 a^{-4} -32 z^8 a^{-6} +12 z^8 a^{-8} -31 z^8+a^3 z^7-22 a z^7-36 z^7 a^{-1} -41 z^7 a^{-3} -67 z^7 a^{-5} -34 z^7 a^{-7} +5 z^7 a^{-9} -10 a^2 z^6+136 z^6 a^{-2} +130 z^6 a^{-4} +16 z^6 a^{-6} -19 z^6 a^{-8} +z^6 a^{-10} +32 z^6-3 a^3 z^5+19 a z^5+62 z^5 a^{-1} +98 z^5 a^{-3} +87 z^5 a^{-5} +22 z^5 a^{-7} -7 z^5 a^{-9} +7 a^2 z^4-101 z^4 a^{-2} -78 z^4 a^{-4} -4 z^4 a^{-6} +8 z^4 a^{-8} -z^4 a^{-10} -29 z^4+3 a^3 z^3-11 a z^3-50 z^3 a^{-1} -72 z^3 a^{-3} -45 z^3 a^{-5} -7 z^3 a^{-7} +2 z^3 a^{-9} -a^2 z^2+46 z^2 a^{-2} +32 z^2 a^{-4} +3 z^2 a^{-6} -z^2 a^{-8} +17 z^2-a^3 z+4 a z+16 z a^{-1} +21 z a^{-3} +10 z a^{-5} -13 a^{-2} -8 a^{-4} - a^{-6} -5 }[/math] |
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