K13a787
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Polynomial invariants
| Jones polynomial | Data:K13a787/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-13 t^3+38 t^2-66 t+79-66 t^{-1} +38 t^{-2} -13 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a787/Conway Polynomial |
| Determinant | 317 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^8+z^8-2 a^4 z^6+2 a^2 z^6-z^6 a^{-2} +4 z^6+a^6 z^4-4 a^4 z^4-2 a^2 z^4-3 z^4 a^{-2} +8 z^4+a^6 z^2+a^4 z^2-7 a^2 z^2-3 z^2 a^{-2} +9 z^2-a^6+3 a^4-4 a^2- a^{-2} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^4 z^{12}+2 a^2 z^{12}+7 a^5 z^{11}+15 a^3 z^{11}+8 a z^{11}+9 a^6 z^{10}+21 a^4 z^{10}+27 a^2 z^{10}+15 z^{10}+5 a^7 z^9-7 a^5 z^9-15 a^3 z^9+15 a z^9+18 z^9 a^{-1} +a^8 z^8-30 a^6 z^8-81 a^4 z^8-76 a^2 z^8+15 z^8 a^{-2} -11 z^8-18 a^7 z^7-37 a^5 z^7-60 a^3 z^7-77 a z^7-27 z^7 a^{-1} +9 z^7 a^{-3} -3 a^8 z^6+28 a^6 z^6+74 a^4 z^6+41 a^2 z^6-22 z^6 a^{-2} +4 z^6 a^{-4} -28 z^6+21 a^7 z^5+62 a^5 z^5+93 a^3 z^5+78 a z^5+15 z^5 a^{-1} -10 z^5 a^{-3} +z^5 a^{-5} +3 a^8 z^4-4 a^6 z^4-12 a^4 z^4+16 a^2 z^4+17 z^4 a^{-2} -4 z^4 a^{-4} +42 z^4-8 a^7 z^3-27 a^5 z^3-43 a^3 z^3-31 a z^3-z^3 a^{-1} +5 z^3 a^{-3} -z^3 a^{-5} -a^8 z^2-3 a^6 z^2-8 a^4 z^2-20 a^2 z^2-6 z^2 a^{-2} +z^2 a^{-4} -21 z^2+3 a^5 z+6 a^3 z+3 a z-z a^{-1} -z a^{-3} +a^6+3 a^4+4 a^2+ a^{-2} +4 }[/math] |
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