Atkin-Lehner |
2+ 3+ 5- 7- 13- |
Signs for the Atkin-Lehner involutions |
Class |
57330l |
Isogeny class |
Conductor |
57330 |
Conductor |
∏ cp |
160 |
Product of Tamagawa factors cp |
deg |
163840 |
Modular degree for the optimal curve |
Δ |
13225171050000 = 24 · 33 · 55 · 73 · 134 |
Discriminant |
Eigenvalues |
2+ 3+ 5- 7- -6 13- -6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-6099,56293] |
[a1,a2,a3,a4,a6] |
Generators |
[-78:269:1] [-474:3877:8] |
Generators of the group modulo torsion |
j |
2709453996621/1428050000 |
j-invariant |
L |
7.6330779879941 |
L(r)(E,1)/r! |
Ω |
0.62143513043034 |
Real period |
R |
0.30707460900649 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000003 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
57330de1 57330e1 |
Quadratic twists by: -3 -7 |