K13a4355
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Polynomial invariants
| Jones polynomial | Data:K13a4355/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+15 t^3-50 t^2+97 t-119+97 t^{-1} -50 t^{-2} +15 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a4355/Conway Polynomial |
| Determinant | 447 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -3 z^6 a^{-2} -z^6 a^{-4} +2 z^6 a^{-6} +z^6-6 z^4 a^{-2} +2 z^4 a^{-4} +3 z^4 a^{-6} -z^4 a^{-8} +2 z^4-5 z^2 a^{-2} +3 z^2 a^{-4} +z^2 a^{-6} -z^2 a^{-8} +2 z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 5 z^{12} a^{-4} +5 z^{12} a^{-6} +17 z^{11} a^{-3} +31 z^{11} a^{-5} +14 z^{11} a^{-7} +25 z^{10} a^{-2} +39 z^{10} a^{-4} +31 z^{10} a^{-6} +17 z^{10} a^{-8} +22 z^9 a^{-1} -4 z^9 a^{-3} -47 z^9 a^{-5} -9 z^9 a^{-7} +12 z^9 a^{-9} -41 z^8 a^{-2} -110 z^8 a^{-4} -94 z^8 a^{-6} -33 z^8 a^{-8} +5 z^8 a^{-10} +13 z^8+5 a z^7-39 z^7 a^{-1} -47 z^7 a^{-3} -7 z^7 a^{-5} -32 z^7 a^{-7} -27 z^7 a^{-9} +z^7 a^{-11} +a^2 z^6+19 z^6 a^{-2} +92 z^6 a^{-4} +79 z^6 a^{-6} +16 z^6 a^{-8} -11 z^6 a^{-10} -20 z^6-6 a z^5+28 z^5 a^{-1} +57 z^5 a^{-3} +37 z^5 a^{-5} +37 z^5 a^{-7} +21 z^5 a^{-9} -2 z^5 a^{-11} -a^2 z^4+9 z^4 a^{-2} -23 z^4 a^{-4} -28 z^4 a^{-6} +8 z^4 a^{-10} +11 z^4+a z^3-9 z^3 a^{-1} -22 z^3 a^{-3} -22 z^3 a^{-5} -18 z^3 a^{-7} -7 z^3 a^{-9} +z^3 a^{-11} -8 z^2 a^{-2} -2 z^2 a^{-4} +2 z^2 a^{-6} -2 z^2 a^{-8} -2 z^2 a^{-10} -4 z^2+z a^{-1} +4 z a^{-3} +6 z a^{-5} +4 z a^{-7} +z a^{-9} +1 }[/math] |
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