Atkin-Lehner |
3- 11- 13- 53+ |
Signs for the Atkin-Lehner involutions |
Class |
68211g |
Isogeny class |
Conductor |
68211 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
141312 |
Modular degree for the optimal curve |
Δ |
-2870025095223 = -1 · 310 · 113 · 13 · 532 |
Discriminant |
Eigenvalues |
-1 3- -4 0 11- 13- -2 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,1813,-76350] |
[a1,a2,a3,a4,a6] |
Generators |
[286:1311:8] [56:-474:1] |
Generators of the group modulo torsion |
j |
904511618711/3936934287 |
j-invariant |
L |
5.1678579933494 |
L(r)(E,1)/r! |
Ω |
0.40650933362697 |
Real period |
R |
2.1187943161467 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000102 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
22737b1 |
Quadratic twists by: -3 |