Atkin-Lehner |
2- 3- 5+ 7- 67- |
Signs for the Atkin-Lehner involutions |
Class |
42210t |
Isogeny class |
Conductor |
42210 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
688128 |
Modular degree for the optimal curve |
Δ |
1652010315153408000 = 232 · 38 · 53 · 7 · 67 |
Discriminant |
Eigenvalues |
2- 3- 5+ 7- 0 -2 -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-295538,-152719] |
[a1,a2,a3,a4,a6] |
Generators |
[-287:7951:1] |
Generators of the group modulo torsion |
j |
3915928883952048601/2266132119552000 |
j-invariant |
L |
8.4297725404822 |
L(r)(E,1)/r! |
Ω |
0.22480679277907 |
Real period |
R |
2.3436159435691 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000009 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
14070f1 |
Quadratic twists by: -3 |