Atkin-Lehner |
2- 3- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
69192be |
Isogeny class |
Conductor |
69192 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
1547520 |
Modular degree for the optimal curve |
Δ |
-3820078487313340416 = -1 · 211 · 37 · 318 |
Discriminant |
Eigenvalues |
2- 3- -2 -5 -3 0 -6 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-625611,212409830] |
[a1,a2,a3,a4,a6] |
Generators |
[442:4716:1] |
Generators of the group modulo torsion |
j |
-21266/3 |
j-invariant |
L |
2.5378791085894 |
L(r)(E,1)/r! |
Ω |
0.24027319219909 |
Real period |
R |
5.2812365068203 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000336 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
23064a1 69192bk1 |
Quadratic twists by: -3 -31 |