K13a1023
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Polynomial invariants
| Jones polynomial | Data:K13a1023/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 6 t^3-29 t^2+65 t-83+65 t^{-1} -29 t^{-2} +6 t^{-3} }[/math] |
| Conway polynomial | Data:K13a1023/Conway Polynomial |
| Determinant | 283 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ 3 z^6 a^{-2} +2 z^6 a^{-4} +z^6-a^2 z^4+7 z^4 a^{-2} +4 z^4 a^{-4} -3 z^4 a^{-6} -a^2 z^2+6 z^2 a^{-2} +5 z^2 a^{-4} -6 z^2 a^{-6} +z^2 a^{-8} -2 z^2+2 a^{-2} +3 a^{-4} -4 a^{-6} + a^{-8} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{12} a^{-2} +2 z^{12} a^{-4} +7 z^{11} a^{-1} +13 z^{11} a^{-3} +6 z^{11} a^{-5} +16 z^{10} a^{-2} +14 z^{10} a^{-4} +8 z^{10} a^{-6} +10 z^{10}+8 a z^9-8 z^9 a^{-1} -25 z^9 a^{-3} -z^9 a^{-5} +8 z^9 a^{-7} +4 a^2 z^8-63 z^8 a^{-2} -42 z^8 a^{-4} -4 z^8 a^{-6} +7 z^8 a^{-8} -28 z^8+a^3 z^7-24 a z^7-19 z^7 a^{-1} +8 z^7 a^{-3} -7 z^7 a^{-5} -5 z^7 a^{-7} +4 z^7 a^{-9} -12 a^2 z^6+84 z^6 a^{-2} +45 z^6 a^{-4} -14 z^6 a^{-6} -12 z^6 a^{-8} +z^6 a^{-10} +26 z^6-3 a^3 z^5+22 a z^5+37 z^5 a^{-1} +17 z^5 a^{-3} -3 z^5 a^{-5} -17 z^5 a^{-7} -9 z^5 a^{-9} +9 a^2 z^4-50 z^4 a^{-2} -14 z^4 a^{-4} +18 z^4 a^{-6} +5 z^4 a^{-8} -2 z^4 a^{-10} -16 z^4+2 a^3 z^3-11 a z^3-23 z^3 a^{-1} -10 z^3 a^{-3} +14 z^3 a^{-5} +21 z^3 a^{-7} +7 z^3 a^{-9} -2 a^2 z^2+14 z^2 a^{-2} -4 z^2 a^{-4} -12 z^2 a^{-6} -z^2 a^{-8} +z^2 a^{-10} +6 z^2+2 a z+4 z a^{-1} +z a^{-3} -7 z a^{-5} -8 z a^{-7} -2 z a^{-9} -2 a^{-2} +3 a^{-4} +4 a^{-6} + a^{-8} -1 }[/math] |
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