Atkin-Lehner |
2+ 5+ 19+ 61+ |
Signs for the Atkin-Lehner involutions |
Class |
57950b |
Isogeny class |
Conductor |
57950 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
74880 |
Modular degree for the optimal curve |
Δ |
72437500000 = 25 · 59 · 19 · 61 |
Discriminant |
Eigenvalues |
2+ 3 5+ -2 -2 0 -1 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-1042,116] |
[a1,a2,a3,a4,a6] |
Generators |
[3:11:27] |
Generators of the group modulo torsion |
j |
8012006001/4636000 |
j-invariant |
L |
7.4877559021622 |
L(r)(E,1)/r! |
Ω |
0.92161522650783 |
Real period |
R |
4.0623004516881 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000416 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
11590p1 |
Quadratic twists by: 5 |