Atkin-Lehner |
2- 3- 5+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
40050be |
Isogeny class |
Conductor |
40050 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
393216 |
Modular degree for the optimal curve |
Δ |
57024316406250000 = 24 · 38 · 514 · 89 |
Discriminant |
Eigenvalues |
2- 3- 5+ -4 -4 -2 2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-191255,30121247] |
[a1,a2,a3,a4,a6] |
Generators |
[309:520:1] |
Generators of the group modulo torsion |
j |
67922306042401/5006250000 |
j-invariant |
L |
6.8260714883753 |
L(r)(E,1)/r! |
Ω |
0.3452430983235 |
Real period |
R |
2.4714728265104 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
13350h1 8010b1 |
Quadratic twists by: -3 5 |