K13a3690
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Polynomial invariants
| Jones polynomial | Data:K13a3690/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-12 t^3+36 t^2-62 t+73-62 t^{-1} +36 t^{-2} -12 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a3690/Conway Polynomial |
| Determinant | 297 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^8-3 z^4 a^8-4 z^2 a^8-2 a^8+z^8 a^6+4 z^6 a^6+8 z^4 a^6+8 z^2 a^6+a^6+z^8 a^4+3 z^6 a^4+4 z^4 a^4+5 z^2 a^4+3 a^4-2 z^6 a^2-6 z^4 a^2-5 z^2 a^2-a^2+z^4+2 z^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-z^3 a^{13}+4 z^6 a^{12}-3 z^4 a^{12}+10 z^7 a^{11}-12 z^5 a^{11}+8 z^3 a^{11}-2 z a^{11}+17 z^8 a^{10}-27 z^6 a^{10}+21 z^4 a^{10}-4 z^2 a^{10}+20 z^9 a^9-34 z^7 a^9+25 z^5 a^9-7 z^3 a^9+2 z a^9+16 z^{10} a^8-20 z^8 a^8+3 z^6 a^8-z^4 a^8+4 z^2 a^8-2 a^8+8 z^{11} a^7+7 z^9 a^7-42 z^7 a^7+35 z^5 a^7-18 z^3 a^7+2 z a^7+2 z^{12} a^6+20 z^{10} a^6-55 z^8 a^6+43 z^6 a^6-27 z^4 a^6+10 z^2 a^6-a^6+13 z^{11} a^5-24 z^9 a^5+5 z^7 a^5-7 z^5 a^5+12 z^3 a^5-6 z a^5+2 z^{12} a^4+10 z^{10} a^4-39 z^8 a^4+31 z^6 a^4-8 z^4 a^4+3 z^2 a^4+3 a^4+5 z^{11} a^3-7 z^9 a^3-14 z^7 a^3+20 z^5 a^3+4 z^3 a^3-6 z a^3+6 z^{10} a^2-20 z^8 a^2+18 z^6 a^2-z^4 a^2-z^2 a^2+a^2+4 z^9 a-17 z^7 a+24 z^5 a-10 z^3 a-2 z a+z^8-4 z^6+5 z^4-2 z^2 }[/math] |
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