Atkin-Lehner |
2- 23- 53+ |
Signs for the Atkin-Lehner involutions |
Class |
112148c |
Isogeny class |
Conductor |
112148 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
684288 |
Modular degree for the optimal curve |
Δ |
-80951005216793072 = -1 · 24 · 239 · 532 |
Discriminant |
Eigenvalues |
2- -1 2 2 4 -1 0 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,2998,13687777] |
[a1,a2,a3,a4,a6] |
Generators |
[8:3703:1] |
Generators of the group modulo torsion |
j |
1257728/34177103 |
j-invariant |
L |
7.6035784002147 |
L(r)(E,1)/r! |
Ω |
0.27051579034537 |
Real period |
R |
2.3423088591492 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000017131 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
4876c1 |
Quadratic twists by: -23 |