Atkin-Lehner |
2- 3+ 5- 13+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
86190cd |
Isogeny class |
Conductor |
86190 |
Conductor |
∏ cp |
990 |
Product of Tamagawa factors cp |
deg |
1140480 |
Modular degree for the optimal curve |
Δ |
72741988051200000 = 211 · 34 · 55 · 134 · 173 |
Discriminant |
Eigenvalues |
2- 3+ 5- -3 -5 13+ 17- -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-107065,-3709945] |
[a1,a2,a3,a4,a6] |
Generators |
[-307:738:1] [-47:-1082:1] |
Generators of the group modulo torsion |
j |
4752182606640001/2546899200000 |
j-invariant |
L |
13.473908618031 |
L(r)(E,1)/r! |
Ω |
0.28077296508213 |
Real period |
R |
0.048473358897221 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000014 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
86190f1 |
Quadratic twists by: 13 |