Atkin-Lehner |
3- 7+ 17- 23- |
Signs for the Atkin-Lehner involutions |
Class |
8211i |
Isogeny class |
Conductor |
8211 |
Conductor |
∏ cp |
126 |
Product of Tamagawa factors cp |
deg |
24192 |
Modular degree for the optimal curve |
Δ |
-6405825961773 = -1 · 37 · 72 · 173 · 233 |
Discriminant |
Eigenvalues |
-1 3- -2 7+ -5 -5 17- -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-15299,737190] |
[a1,a2,a3,a4,a6] |
Generators |
[-143:148:1] [-65:1240:1] |
Generators of the group modulo torsion |
j |
-396017721037004977/6405825961773 |
j-invariant |
L |
3.8759143559704 |
L(r)(E,1)/r! |
Ω |
0.75380626075382 |
Real period |
R |
0.040807866223629 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000003 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
24633c1 57477g1 |
Quadratic twists by: -3 -7 |