Atkin-Lehner |
2+ 3- 7- 19- |
Signs for the Atkin-Lehner involutions |
Class |
38304x |
Isogeny class |
Conductor |
38304 |
Conductor |
∏ cp |
192 |
Product of Tamagawa factors cp |
deg |
442368 |
Modular degree for the optimal curve |
Δ |
57942224578695744 = 26 · 310 · 76 · 194 |
Discriminant |
Eigenvalues |
2+ 3- -2 7- 0 -6 -2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-372441,86715200] |
[a1,a2,a3,a4,a6] |
Generators |
[-571:10640:1] [163:5508:1] |
Generators of the group modulo torsion |
j |
122458422894369472/1241902961649 |
j-invariant |
L |
8.1748552331035 |
L(r)(E,1)/r! |
Ω |
0.35366329090378 |
Real period |
R |
1.9262330968843 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
38304j1 76608ex2 12768p1 |
Quadratic twists by: -4 8 -3 |