Atkin-Lehner |
2- 3- 5+ 23- 31- |
Signs for the Atkin-Lehner involutions |
Class |
128340i |
Isogeny class |
Conductor |
128340 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
645120 |
Modular degree for the optimal curve |
Δ |
255714690690000 = 24 · 37 · 54 · 233 · 312 |
Discriminant |
Eigenvalues |
2- 3- 5+ 2 4 2 -6 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-111828,14373173] |
[a1,a2,a3,a4,a6] |
Generators |
[211:414:1] |
Generators of the group modulo torsion |
j |
13259522191507456/21923413125 |
j-invariant |
L |
7.9820153052029 |
L(r)(E,1)/r! |
Ω |
0.55315929223013 |
Real period |
R |
1.2024889706827 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999912246 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
42780d1 |
Quadratic twists by: -3 |