Atkin-Lehner |
2- 3+ 5- 19- 67- |
Signs for the Atkin-Lehner involutions |
Class |
38190bb |
Isogeny class |
Conductor |
38190 |
Conductor |
∏ cp |
204 |
Product of Tamagawa factors cp |
deg |
1605888 |
Modular degree for the optimal curve |
Δ |
-2599991820288000 = -1 · 217 · 38 · 53 · 192 · 67 |
Discriminant |
Eigenvalues |
2- 3+ 5- -1 3 6 -4 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-13311055,18686929877] |
[a1,a2,a3,a4,a6] |
Generators |
[2267:-14094:1] |
Generators of the group modulo torsion |
j |
-260832166013005415555364721/2599991820288000 |
j-invariant |
L |
8.7393445023842 |
L(r)(E,1)/r! |
Ω |
0.31866163716176 |
Real period |
R |
0.13443702986297 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999987 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
114570p1 |
Quadratic twists by: -3 |