Atkin-Lehner |
2- 3+ 7+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
52332a |
Isogeny class |
Conductor |
52332 |
Conductor |
∏ cp |
3 |
Product of Tamagawa factors cp |
deg |
344736 |
Modular degree for the optimal curve |
Δ |
2585268083043072 = 28 · 39 · 78 · 89 |
Discriminant |
Eigenvalues |
2- 3+ 0 7+ -3 -4 2 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-328708,-72386936] |
[a1,a2,a3,a4,a6] |
Generators |
[-334:174:1] [-330:202:1] |
Generators of the group modulo torsion |
j |
2661531250000/1751787 |
j-invariant |
L |
8.2864277203355 |
L(r)(E,1)/r! |
Ω |
0.19939489452549 |
Real period |
R |
13.852624361412 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
52332i1 |
Quadratic twists by: -7 |