Atkin-Lehner |
2+ 3- 5+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
69600r |
Isogeny class |
Conductor |
69600 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
49152 |
Modular degree for the optimal curve |
Δ |
37845000000 = 26 · 32 · 57 · 292 |
Discriminant |
Eigenvalues |
2+ 3- 5+ -2 -4 -2 -4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-1258,13988] |
[a1,a2,a3,a4,a6] |
Generators |
[-32:150:1] [-16:174:1] |
Generators of the group modulo torsion |
j |
220348864/37845 |
j-invariant |
L |
11.438316295651 |
L(r)(E,1)/r! |
Ω |
1.1003202520464 |
Real period |
R |
1.2994303561135 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000007 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69600a1 13920x1 |
Quadratic twists by: -4 5 |