Atkin-Lehner |
2+ 3- 13+ 19+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
128934h |
Isogeny class |
Conductor |
128934 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
189952 |
Modular degree for the optimal curve |
Δ |
-38098449792 = -1 · 27 · 37 · 13 · 192 · 29 |
Discriminant |
Eigenvalues |
2+ 3- 4 -2 3 13+ -3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-180,-9392] |
[a1,a2,a3,a4,a6] |
Generators |
[59:398:1] |
Generators of the group modulo torsion |
j |
-887503681/52261248 |
j-invariant |
L |
6.9864123652575 |
L(r)(E,1)/r! |
Ω |
0.5067793006433 |
Real period |
R |
1.723238369726 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000112284 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
42978f1 |
Quadratic twists by: -3 |