Atkin-Lehner |
3- 11+ 19- 53- |
Signs for the Atkin-Lehner involutions |
Class |
33231g |
Isogeny class |
Conductor |
33231 |
Conductor |
∏ cp |
18 |
Product of Tamagawa factors cp |
deg |
35136 |
Modular degree for the optimal curve |
Δ |
1187642709 = 33 · 112 · 193 · 53 |
Discriminant |
Eigenvalues |
-1 3- -3 -3 11+ 4 0 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-2862,58671] |
[a1,a2,a3,a4,a6] |
Generators |
[-34:359:1] [-15:321:1] |
Generators of the group modulo torsion |
j |
2592639207601633/1187642709 |
j-invariant |
L |
5.281133090896 |
L(r)(E,1)/r! |
Ω |
1.5163294893738 |
Real period |
R |
0.19349111448637 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000003 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
99693h1 |
Quadratic twists by: -3 |