Atkin-Lehner |
2+ 37- 43+ |
Signs for the Atkin-Lehner involutions |
Class |
50912a |
Isogeny class |
Conductor |
50912 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
78336 |
Modular degree for the optimal curve |
Δ |
383620698112 = 212 · 373 · 432 |
Discriminant |
Eigenvalues |
2+ -1 0 -3 -5 -2 -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-22253,1284805] |
[a1,a2,a3,a4,a6] |
Generators |
[-76:1591:1] [35:740:1] |
Generators of the group modulo torsion |
j |
297542483776000/93657397 |
j-invariant |
L |
6.8578748360963 |
L(r)(E,1)/r! |
Ω |
0.93139830182236 |
Real period |
R |
0.61358236165623 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999987 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
50912b1 101824h1 |
Quadratic twists by: -4 8 |