K13a4767
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Polynomial invariants
| Jones polynomial | Data:K13a4767/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -3 t^4+15 t^3-32 t^2+49 t-57+49 t^{-1} -32 t^{-2} +15 t^{-3} -3 t^{-4} }[/math] |
| Conway polynomial | Data:K13a4767/Conway Polynomial |
| Determinant | 255 |
| Signature | -6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^{12}-3 z^2 a^{12}-2 a^{12}+3 z^6 a^{10}+12 z^4 a^{10}+14 z^2 a^{10}+4 a^{10}-2 z^8 a^8-10 z^6 a^8-18 z^4 a^8-15 z^2 a^8-5 a^8-z^8 a^6-3 z^6 a^6+z^4 a^6+8 z^2 a^6+4 a^6+z^6 a^4+4 z^4 a^4+4 z^2 a^4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{17}-z^3 a^{17}+4 z^6 a^{16}-4 z^4 a^{16}+9 z^7 a^{15}-12 z^5 a^{15}+6 z^3 a^{15}-2 z a^{15}+14 z^8 a^{14}-23 z^6 a^{14}+16 z^4 a^{14}-4 z^2 a^{14}+16 z^9 a^{13}-29 z^7 a^{13}+20 z^5 a^{13}-3 z^3 a^{13}+2 z a^{13}+13 z^{10} a^{12}-20 z^8 a^{12}+5 z^6 a^{12}+5 z^4 a^{12}+3 z^2 a^{12}-2 a^{12}+7 z^{11} a^{11}-30 z^7 a^{11}+36 z^5 a^{11}-15 z^3 a^{11}+2 z a^{11}+2 z^{12} a^{10}+14 z^{10} a^{10}-54 z^8 a^{10}+70 z^6 a^{10}-52 z^4 a^{10}+18 z^2 a^{10}-4 a^{10}+12 z^{11} a^9-35 z^9 a^9+39 z^7 a^9-30 z^5 a^9+10 z^3 a^9-2 z a^9+2 z^{12} a^8+6 z^{10} a^8-41 z^8 a^8+71 z^6 a^8-68 z^4 a^8+31 z^2 a^8-5 a^8+5 z^{11} a^7-16 z^9 a^7+18 z^7 a^7-16 z^5 a^7+9 z^3 a^7+5 z^{10} a^6-20 z^8 a^6+28 z^6 a^6-23 z^4 a^6+16 z^2 a^6-4 a^6+3 z^9 a^5-13 z^7 a^5+17 z^5 a^5-6 z^3 a^5+z^8 a^4-5 z^6 a^4+8 z^4 a^4-4 z^2 a^4 }[/math] |
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