K13a1488
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Polynomial invariants
| Jones polynomial | Data:K13a1488/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+12 t^3-34 t^2+61 t-73+61 t^{-1} -34 t^{-2} +12 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a1488/Conway Polynomial |
| Determinant | 291 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8+a^2 z^6-3 z^6 a^{-2} +2 z^6 a^{-4} -4 z^6+3 a^2 z^4-3 z^4 a^{-2} +6 z^4 a^{-4} -z^4 a^{-6} -7 z^4+3 a^2 z^2+6 z^2 a^{-4} -2 z^2 a^{-6} -6 z^2+a^2+2 a^{-2} + a^{-4} - a^{-6} -2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{12} a^{-2} +2 z^{12}+6 a z^{11}+14 z^{11} a^{-1} +8 z^{11} a^{-3} +7 a^2 z^{10}+23 z^{10} a^{-2} +15 z^{10} a^{-4} +15 z^{10}+4 a^3 z^9-10 a z^9-24 z^9 a^{-1} +7 z^9 a^{-3} +17 z^9 a^{-5} +a^4 z^8-25 a^2 z^8-77 z^8 a^{-2} -21 z^8 a^{-4} +14 z^8 a^{-6} -68 z^8-16 a^3 z^7-19 a z^7-26 z^7 a^{-1} -59 z^7 a^{-3} -27 z^7 a^{-5} +9 z^7 a^{-7} -4 a^4 z^6+27 a^2 z^6+74 z^6 a^{-2} +2 z^6 a^{-4} -19 z^6 a^{-6} +4 z^6 a^{-8} +80 z^6+21 a^3 z^5+42 a z^5+64 z^5 a^{-1} +72 z^5 a^{-3} +17 z^5 a^{-5} -11 z^5 a^{-7} +z^5 a^{-9} +5 a^4 z^4-11 a^2 z^4-30 z^4 a^{-2} +9 z^4 a^{-4} +11 z^4 a^{-6} -4 z^4 a^{-8} -40 z^4-11 a^3 z^3-25 a z^3-40 z^3 a^{-1} -38 z^3 a^{-3} -5 z^3 a^{-5} +6 z^3 a^{-7} -z^3 a^{-9} -2 a^4 z^2+3 a^2 z^2+5 z^2 a^{-2} -6 z^2 a^{-4} -3 z^2 a^{-6} +z^2 a^{-8} +12 z^2+2 a^3 z+6 a z+9 z a^{-1} +8 z a^{-3} +2 z a^{-5} -z a^{-7} -a^2-2 a^{-2} + a^{-4} + a^{-6} -2 }[/math] |
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