Atkin-Lehner |
2- 3- 7+ 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
42042cy |
Isogeny class |
Conductor |
42042 |
Conductor |
∏ cp |
1620 |
Product of Tamagawa factors cp |
deg |
518400 |
Modular degree for the optimal curve |
Δ |
-80752750541438976 = -1 · 215 · 33 · 74 · 113 · 134 |
Discriminant |
Eigenvalues |
2- 3- -3 7+ 11- 13- -3 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-25922,13764036] |
[a1,a2,a3,a4,a6] |
Generators |
[-260:1846:1] |
Generators of the group modulo torsion |
j |
-802302449299393/33632965656576 |
j-invariant |
L |
9.1496577183329 |
L(r)(E,1)/r! |
Ω |
0.28461179080988 |
Real period |
R |
0.17859917758103 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
126126bg1 42042cl1 |
Quadratic twists by: -3 -7 |