Atkin-Lehner |
2- 3+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
50784w |
Isogeny class |
Conductor |
50784 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
50688 |
Modular degree for the optimal curve |
Δ |
85268672064 = 26 · 32 · 236 |
Discriminant |
Eigenvalues |
2- 3+ -2 -4 4 -2 6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1234,9424] |
[a1,a2,a3,a4,a6] |
Generators |
[58:360:1] |
Generators of the group modulo torsion |
j |
21952/9 |
j-invariant |
L |
3.2479830475106 |
L(r)(E,1)/r! |
Ω |
0.97703188984221 |
Real period |
R |
3.3243367809108 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999549 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
50784q1 101568be2 96b1 |
Quadratic twists by: -4 8 -23 |