K13a1088
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Polynomial invariants
| Jones polynomial | Data:K13a1088/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+15 t^3-49 t^2+91 t-109+91 t^{-1} -49 t^{-2} +15 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a1088/Conway Polynomial |
| Determinant | 423 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8+a^2 z^6-z^6 a^{-2} +2 z^6 a^{-4} -3 z^6+2 a^2 z^4+3 z^4 a^{-2} +3 z^4 a^{-4} -z^4 a^{-6} -6 z^4+2 a^2 z^2+5 z^2 a^{-2} -z^2 a^{-6} -8 z^2+2 a^2+2 a^{-2} -3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 z^{12} a^{-2} +4 z^{12}+11 a z^{11}+28 z^{11} a^{-1} +17 z^{11} a^{-3} +11 a^2 z^{10}+49 z^{10} a^{-2} +32 z^{10} a^{-4} +28 z^{10}+5 a^3 z^9-18 a z^9-43 z^9 a^{-1} +16 z^9 a^{-3} +36 z^9 a^{-5} +a^4 z^8-35 a^2 z^8-150 z^8 a^{-2} -42 z^8 a^{-4} +27 z^8 a^{-6} -117 z^8-16 a^3 z^7-21 a z^7-49 z^7 a^{-1} -118 z^7 a^{-3} -60 z^7 a^{-5} +14 z^7 a^{-7} -3 a^4 z^6+38 a^2 z^6+121 z^6 a^{-2} -8 z^6 a^{-4} -36 z^6 a^{-6} +5 z^6 a^{-8} +129 z^6+18 a^3 z^5+49 a z^5+96 z^5 a^{-1} +114 z^5 a^{-3} +38 z^5 a^{-5} -10 z^5 a^{-7} +z^5 a^{-9} +3 a^4 z^4-17 a^2 z^4-38 z^4 a^{-2} +21 z^4 a^{-4} +21 z^4 a^{-6} -z^4 a^{-8} -57 z^4-8 a^3 z^3-23 a z^3-42 z^3 a^{-1} -43 z^3 a^{-3} -13 z^3 a^{-5} +3 z^3 a^{-7} -a^4 z^2+5 a^2 z^2+8 z^2 a^{-2} -7 z^2 a^{-4} -5 z^2 a^{-6} +16 z^2+a^3 z+3 a z+7 z a^{-1} +7 z a^{-3} +2 z a^{-5} -2 a^2-2 a^{-2} -3 }[/math] |
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