K13a2222
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Polynomial invariants
| Jones polynomial | Data:K13a2222/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-14 t^3+46 t^2-88 t+109-88 t^{-1} +46 t^{-2} -14 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a2222/Conway Polynomial |
| Determinant | 409 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^8+z^8-a^4 z^6+3 a^2 z^6-2 z^6 a^{-2} +2 z^6-2 a^4 z^4+5 a^2 z^4-4 z^4 a^{-2} +z^4 a^{-4} +2 z^4-2 a^4 z^2+4 a^2 z^2-3 z^2 a^{-2} +z^2 a^{-4} +2 z^2-a^4+a^2- a^{-2} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^2 z^{12}+3 z^{12}+11 a^3 z^{11}+23 a z^{11}+12 z^{11} a^{-1} +16 a^4 z^{10}+36 a^2 z^{10}+20 z^{10} a^{-2} +40 z^{10}+12 a^5 z^9+2 a^3 z^9-18 a z^9+11 z^9 a^{-1} +19 z^9 a^{-3} +5 a^6 z^8-34 a^4 z^8-109 a^2 z^8-29 z^8 a^{-2} +12 z^8 a^{-4} -111 z^8+a^7 z^7-29 a^5 z^7-59 a^3 z^7-64 a z^7-73 z^7 a^{-1} -33 z^7 a^{-3} +5 z^7 a^{-5} -11 a^6 z^6+22 a^4 z^6+108 a^2 z^6+9 z^6 a^{-2} -19 z^6 a^{-4} +z^6 a^{-6} +104 z^6-2 a^7 z^5+24 a^5 z^5+72 a^3 z^5+102 a z^5+84 z^5 a^{-1} +21 z^5 a^{-3} -7 z^5 a^{-5} +7 a^6 z^4-11 a^4 z^4-52 a^2 z^4+6 z^4 a^{-2} +9 z^4 a^{-4} -z^4 a^{-6} -38 z^4+a^7 z^3-11 a^5 z^3-37 a^3 z^3-50 a z^3-33 z^3 a^{-1} -6 z^3 a^{-3} +2 z^3 a^{-5} -a^6 z^2+5 a^4 z^2+12 a^2 z^2-4 z^2 a^{-2} -2 z^2 a^{-4} +4 z^2+3 a^5 z+7 a^3 z+7 a z+3 z a^{-1} -a^4-a^2+ a^{-2} +2 }[/math] |
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