K13a1065
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Polynomial invariants
| Jones polynomial | Data:K13a1065/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+13 t^3-42 t^2+84 t-105+84 t^{-1} -42 t^{-2} +13 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a1065/Conway Polynomial |
| Determinant | 387 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -4 z^6 a^{-2} -2 z^6 a^{-4} +2 z^6 a^{-6} +z^6-9 z^4 a^{-2} +3 z^4 a^{-6} -z^4 a^{-8} +3 z^4-9 z^2 a^{-2} +6 z^2 a^{-4} +4 z^2-4 a^{-2} +5 a^{-4} -2 a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{12} a^{-4} +3 z^{12} a^{-6} +9 z^{11} a^{-3} +21 z^{11} a^{-5} +12 z^{11} a^{-7} +13 z^{10} a^{-2} +27 z^{10} a^{-4} +33 z^{10} a^{-6} +19 z^{10} a^{-8} +13 z^9 a^{-1} +9 z^9 a^{-3} -21 z^9 a^{-5} -2 z^9 a^{-7} +15 z^9 a^{-9} -8 z^8 a^{-2} -63 z^8 a^{-4} -95 z^8 a^{-6} -43 z^8 a^{-8} +6 z^8 a^{-10} +9 z^8+4 a z^7-19 z^7 a^{-1} -44 z^7 a^{-3} -36 z^7 a^{-5} -52 z^7 a^{-7} -36 z^7 a^{-9} +z^7 a^{-11} +a^2 z^6-20 z^6 a^{-2} +33 z^6 a^{-4} +69 z^6 a^{-6} +22 z^6 a^{-8} -11 z^6 a^{-10} -16 z^6-7 a z^5+10 z^5 a^{-1} +41 z^5 a^{-3} +51 z^5 a^{-5} +49 z^5 a^{-7} +21 z^5 a^{-9} -z^5 a^{-11} -2 a^2 z^4+34 z^4 a^{-2} +17 z^4 a^{-4} -4 z^4 a^{-6} +z^4 a^{-8} +3 z^4 a^{-10} +13 z^4+4 a z^3-z^3 a^{-1} -12 z^3 a^{-3} -13 z^3 a^{-5} -7 z^3 a^{-7} -z^3 a^{-9} +a^2 z^2-20 z^2 a^{-2} -20 z^2 a^{-4} -10 z^2 a^{-6} -2 z^2 a^{-8} -7 z^2-a z-z a^{-1} -2 z a^{-5} -2 z a^{-7} +4 a^{-2} +5 a^{-4} +2 a^{-6} +2 }[/math] |
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