Atkin-Lehner |
2- 5+ 31+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
57350n |
Isogeny class |
Conductor |
57350 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1336320 |
Modular degree for the optimal curve |
Δ |
-4137806980468750000 = -1 · 24 · 512 · 315 · 37 |
Discriminant |
Eigenvalues |
2- -2 5+ -1 -2 5 2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-865313,-324981383] |
[a1,a2,a3,a4,a6] |
Generators |
[308672:171337739:1] |
Generators of the group modulo torsion |
j |
-4585887564298864201/264819646750000 |
j-invariant |
L |
6.5602321508546 |
L(r)(E,1)/r! |
Ω |
0.078005220993521 |
Real period |
R |
10.512488887577 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999998715 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
11470a1 |
Quadratic twists by: 5 |