Atkin-Lehner |
31+ 41+ |
Signs for the Atkin-Lehner involutions |
Class |
52111a |
Isogeny class |
Conductor |
52111 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
787200 |
Modular degree for the optimal curve |
Δ |
314614038952596521 = 312 · 419 |
Discriminant |
Eigenvalues |
1 2 2 2 2 0 -4 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-1402829,638367800] |
[a1,a2,a3,a4,a6] |
Generators |
[8438551682445022837537695350:-1738479023291824831931171725:12668311038351622165022888] |
Generators of the group modulo torsion |
j |
932574833/961 |
j-invariant |
L |
12.900179963627 |
L(r)(E,1)/r! |
Ω |
0.30436396224753 |
Real period |
R |
42.384058442291 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
52111b1 |
Quadratic twists by: 41 |