Atkin-Lehner |
2- 3+ 23+ 41- |
Signs for the Atkin-Lehner involutions |
Class |
33948a |
Isogeny class |
Conductor |
33948 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
13248 |
Modular degree for the optimal curve |
Δ |
4751633664 = 28 · 39 · 23 · 41 |
Discriminant |
Eigenvalues |
2- 3+ 1 3 -2 -2 -2 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-432,-972] |
[a1,a2,a3,a4,a6] |
Generators |
[-126:351:8] |
Generators of the group modulo torsion |
j |
1769472/943 |
j-invariant |
L |
6.6187005779785 |
L(r)(E,1)/r! |
Ω |
1.1129235794344 |
Real period |
R |
2.9735647174183 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
33948b1 |
Quadratic twists by: -3 |