K13a4271
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Polynomial invariants
| Jones polynomial | Data:K13a4271/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-22 t^2+53 t-69+53 t^{-1} -22 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | Data:K13a4271/Conway Polynomial |
| Determinant | 227 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^{10}+a^{10}-2 z^4 a^8-3 z^2 a^8-2 a^8+z^6 a^6-z^2 a^6+2 z^6 a^4+4 z^4 a^4+4 z^2 a^4+a^4+z^6 a^2+z^4 a^2+z^2 a^2+a^2-z^4-z^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^8 a^{12}-5 z^6 a^{12}+7 z^4 a^{12}-2 z^2 a^{12}+3 z^9 a^{11}-14 z^7 a^{11}+20 z^5 a^{11}-10 z^3 a^{11}+2 z a^{11}+5 z^{10} a^{10}-22 z^8 a^{10}+32 z^6 a^{10}-21 z^4 a^{10}+7 z^2 a^{10}-a^{10}+5 z^{11} a^9-19 z^9 a^9+25 z^7 a^9-18 z^5 a^9+4 z^3 a^9+z a^9+2 z^{12} a^8+3 z^{10} a^8-33 z^8 a^8+60 z^6 a^8-53 z^4 a^8+19 z^2 a^8-2 a^8+11 z^{11} a^7-39 z^9 a^7+58 z^7 a^7-55 z^5 a^7+26 z^3 a^7-5 z a^7+2 z^{12} a^6+8 z^{10} a^6-35 z^8 a^6+40 z^6 a^6-21 z^4 a^6+5 z^2 a^6+6 z^{11} a^5-4 z^9 a^5-13 z^7 a^5+12 z^5 a^5+5 z^3 a^5-4 z a^5+10 z^{10} a^4-13 z^8 a^4-7 z^6 a^4+22 z^4 a^4-9 z^2 a^4+a^4+13 z^9 a^3-24 z^7 a^3+18 z^5 a^3-4 z^3 a^3+12 z^8 a^2-20 z^6 a^2+13 z^4 a^2-3 z^2 a^2-a^2+8 z^7 a-10 z^5 a+2 z^3 a+4 z^6-5 z^4+z^2+z^5 a^{-1} -z^3 a^{-1} }[/math] |
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