Atkin-Lehner |
2+ 5- 71- |
Signs for the Atkin-Lehner involutions |
Class |
50410f |
Isogeny class |
Conductor |
50410 |
Conductor |
∏ cp |
18 |
Product of Tamagawa factors cp |
deg |
1042848 |
Modular degree for the optimal curve |
Δ |
-5166028249966088000 = -1 · 26 · 53 · 718 |
Discriminant |
Eigenvalues |
2+ 1 5- -1 6 2 -6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,365367,-68763444] |
[a1,a2,a3,a4,a6] |
Generators |
[1055345406502614465:28381338036767161126:3538700096624603] |
Generators of the group modulo torsion |
j |
8353079/8000 |
j-invariant |
L |
6.0055041412875 |
L(r)(E,1)/r! |
Ω |
0.13221339234176 |
Real period |
R |
22.711406291444 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
50410e1 |
Quadratic twists by: -71 |