Atkin-Lehner |
2- 3+ 19+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
13224f |
Isogeny class |
Conductor |
13224 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
699840 |
Modular degree for the optimal curve |
Δ |
-2403499318128 = -1 · 24 · 315 · 192 · 29 |
Discriminant |
Eigenvalues |
2- 3+ -4 3 5 3 3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-19682880,33617534481] |
[a1,a2,a3,a4,a6] |
Generators |
[69168:19:27] |
Generators of the group modulo torsion |
j |
-52707168473774069565112576/150218707383 |
j-invariant |
L |
3.6828827257467 |
L(r)(E,1)/r! |
Ω |
0.38205974978743 |
Real period |
R |
2.4098866262383 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
26448i1 105792z1 39672d1 |
Quadratic twists by: -4 8 -3 |