Atkin-Lehner |
2- 3- 11- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
67518bs |
Isogeny class |
Conductor |
67518 |
Conductor |
∏ cp |
128 |
Product of Tamagawa factors cp |
deg |
614400 |
Modular degree for the optimal curve |
Δ |
53079395516362512 = 24 · 311 · 117 · 312 |
Discriminant |
Eigenvalues |
2- 3- -2 -2 11- -4 2 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-105656,-7175253] |
[a1,a2,a3,a4,a6] |
Generators |
[399:3551:1] [-1538:20367:8] |
Generators of the group modulo torsion |
j |
100999381393/41100048 |
j-invariant |
L |
13.050063654859 |
L(r)(E,1)/r! |
Ω |
0.27438602726764 |
Real period |
R |
1.4862800896802 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
22506d1 6138h1 |
Quadratic twists by: -3 -11 |