Atkin-Lehner |
2+ 3- 37- |
Signs for the Atkin-Lehner involutions |
Class |
21312t |
Isogeny class |
Conductor |
21312 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
67584 |
Modular degree for the optimal curve |
Δ |
-2505145597820928 = -1 · 219 · 317 · 37 |
Discriminant |
Eigenvalues |
2+ 3- 0 3 1 -1 3 -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,9780,-2379152] |
[a1,a2,a3,a4,a6] |
Generators |
[1661:67797:1] |
Generators of the group modulo torsion |
j |
541343375/13108878 |
j-invariant |
L |
5.9265555629721 |
L(r)(E,1)/r! |
Ω |
0.22156915063324 |
Real period |
R |
3.3435134956931 |
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 |
21312cc1 666b1 7104k1 |
Quadratic twists by: -4 8 -3 |