Atkin-Lehner |
2- 3+ 5- 23+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
42780f |
Isogeny class |
Conductor |
42780 |
Conductor |
∏ cp |
36 |
Product of Tamagawa factors cp |
deg |
124416 |
Modular degree for the optimal curve |
Δ |
220455914360400 = 24 · 33 · 52 · 23 · 316 |
Discriminant |
Eigenvalues |
2- 3+ 5- -2 -4 -2 -6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-15105,-12078] |
[a1,a2,a3,a4,a6] |
Generators |
[-113:489:1] [-91:775:1] |
Generators of the group modulo torsion |
j |
23822902301310976/13778494647525 |
j-invariant |
L |
7.7912902021679 |
L(r)(E,1)/r! |
Ω |
0.47155523992013 |
Real period |
R |
1.8358377514766 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
128340k1 |
Quadratic twists by: -3 |