K13a4745
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Polynomial invariants
| Jones polynomial | Data:K13a4745/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ t^5-6 t^4+19 t^3-39 t^2+59 t-67+59 t^{-1} -39 t^{-2} +19 t^{-3} -6 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | Data:K13a4745/Conway Polynomial |
| Determinant | 315 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^{10} a^{-2} +7 z^8 a^{-2} -z^8 a^{-4} -2 z^8+a^2 z^6+20 z^6 a^{-2} -5 z^6 a^{-4} -10 z^6+3 a^2 z^4+28 z^4 a^{-2} -9 z^4 a^{-4} -17 z^4+2 a^2 z^2+19 z^2 a^{-2} -7 z^2 a^{-4} -11 z^2+6 a^{-2} -3 a^{-4} -2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 z^{12} a^{-2} +4 z^{12}+10 a z^{11}+23 z^{11} a^{-1} +13 z^{11} a^{-3} +10 a^2 z^{10}+21 z^{10} a^{-2} +20 z^{10} a^{-4} +11 z^{10}+5 a^3 z^9-29 a z^9-72 z^9 a^{-1} -18 z^9 a^{-3} +20 z^9 a^{-5} +a^4 z^8-37 a^2 z^8-104 z^8 a^{-2} -47 z^8 a^{-4} +15 z^8 a^{-6} -80 z^8-18 a^3 z^7+15 a z^7+66 z^7 a^{-1} -18 z^7 a^{-3} -42 z^7 a^{-5} +9 z^7 a^{-7} -3 a^4 z^6+41 a^2 z^6+145 z^6 a^{-2} +45 z^6 a^{-4} -24 z^6 a^{-6} +4 z^6 a^{-8} +116 z^6+18 a^3 z^5+6 a z^5-19 z^5 a^{-1} +41 z^5 a^{-3} +36 z^5 a^{-5} -11 z^5 a^{-7} +z^5 a^{-9} +2 a^4 z^4-17 a^2 z^4-95 z^4 a^{-2} -22 z^4 a^{-4} +15 z^4 a^{-6} -4 z^4 a^{-8} -73 z^4-4 a^3 z^3-2 a z^3-5 z^3 a^{-1} -22 z^3 a^{-3} -10 z^3 a^{-5} +4 z^3 a^{-7} -z^3 a^{-9} +4 a^2 z^2+30 z^2 a^{-2} +10 z^2 a^{-4} -3 z^2 a^{-6} +21 z^2-a^3 z-a z+2 z a^{-1} +5 z a^{-3} +2 z a^{-5} -z a^{-7} -6 a^{-2} -3 a^{-4} -2 }[/math] |
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