Atkin-Lehner |
3+ 5- 11- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
50325n |
Isogeny class |
Conductor |
50325 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
495360 |
Modular degree for the optimal curve |
Δ |
-115602029296875 = -1 · 36 · 59 · 113 · 61 |
Discriminant |
Eigenvalues |
-2 3+ 5- -2 11- -5 6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-285708,-58687432] |
[a1,a2,a3,a4,a6] |
Generators |
[867:18562:1] |
Generators of the group modulo torsion |
j |
-1320572947632128/59188239 |
j-invariant |
L |
1.745225087453 |
L(r)(E,1)/r! |
Ω |
0.10324943034167 |
Real period |
R |
1.4085833061615 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000307 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
50325bc1 |
Quadratic twists by: 5 |