Atkin-Lehner |
2- 3+ 5- 13- |
Signs for the Atkin-Lehner involutions |
Class |
37440do |
Isogeny class |
Conductor |
37440 |
Conductor |
∏ cp |
192 |
Product of Tamagawa factors cp |
deg |
147456 |
Modular degree for the optimal curve |
Δ |
-379641600000000 = -1 · 214 · 33 · 58 · 133 |
Discriminant |
Eigenvalues |
2- 3+ 5- -2 -4 13- -8 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1212,937584] |
[a1,a2,a3,a4,a6] |
Generators |
[-92:520:1] [-62:880:1] |
Generators of the group modulo torsion |
j |
-445090032/858203125 |
j-invariant |
L |
8.8681186126436 |
L(r)(E,1)/r! |
Ω |
0.43072152885455 |
Real period |
R |
0.42893716408388 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999998 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
37440v1 9360a1 37440dd1 |
Quadratic twists by: -4 8 -3 |