K13a1081
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Polynomial invariants
| Jones polynomial | Data:K13a1081/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-14 t^3+38 t^2-61 t+71-61 t^{-1} +38 t^{-2} -14 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a1081/Conway Polynomial |
| Determinant | 301 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} +z^8 a^{-6} -2 z^6 a^{-2} +2 z^6 a^{-4} +3 z^6 a^{-6} -z^6 a^{-8} -6 z^4 a^{-2} -2 z^4 a^{-4} +3 z^4 a^{-6} -2 z^4 a^{-8} +z^4-4 z^2 a^{-2} -5 z^2 a^{-4} +3 z^2 a^{-6} +3 z^2-3 a^{-4} +2 a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{12} a^{-4} +2 z^{12} a^{-6} +5 z^{11} a^{-3} +14 z^{11} a^{-5} +9 z^{11} a^{-7} +5 z^{10} a^{-2} +12 z^{10} a^{-4} +25 z^{10} a^{-6} +18 z^{10} a^{-8} +3 z^9 a^{-1} -9 z^9 a^{-3} -26 z^9 a^{-5} +8 z^9 a^{-7} +22 z^9 a^{-9} -16 z^8 a^{-2} -57 z^8 a^{-4} -82 z^8 a^{-6} -23 z^8 a^{-8} +19 z^8 a^{-10} +z^8-12 z^7 a^{-1} -9 z^7 a^{-3} -15 z^7 a^{-5} -64 z^7 a^{-7} -34 z^7 a^{-9} +12 z^7 a^{-11} +13 z^6 a^{-2} +75 z^6 a^{-4} +80 z^6 a^{-6} -7 z^6 a^{-8} -25 z^6 a^{-10} +5 z^6 a^{-12} -5 z^6+15 z^5 a^{-1} +21 z^5 a^{-3} +52 z^5 a^{-5} +73 z^5 a^{-7} +14 z^5 a^{-9} -12 z^5 a^{-11} +z^5 a^{-13} -z^4 a^{-2} -50 z^4 a^{-4} -33 z^4 a^{-6} +18 z^4 a^{-8} +8 z^4 a^{-10} -3 z^4 a^{-12} +9 z^4-6 z^3 a^{-1} -11 z^3 a^{-3} -36 z^3 a^{-5} -34 z^3 a^{-7} -z^3 a^{-9} +2 z^3 a^{-11} -z^2 a^{-2} +19 z^2 a^{-4} +8 z^2 a^{-6} -5 z^2 a^{-8} -7 z^2+2 z a^{-3} +8 z a^{-5} +7 z a^{-7} +z a^{-9} -3 a^{-4} -2 a^{-6} +2 }[/math] |
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