Atkin-Lehner |
2- 3- 7- 19- |
Signs for the Atkin-Lehner involutions |
Class |
11172t |
Isogeny class |
Conductor |
11172 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
3072 |
Modular degree for the optimal curve |
Δ |
684128592 = 24 · 38 · 73 · 19 |
Discriminant |
Eigenvalues |
2- 3- 0 7- -4 -2 4 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-233,-624] |
[a1,a2,a3,a4,a6] |
Generators |
[-11:27:1] |
Generators of the group modulo torsion |
j |
256000000/124659 |
j-invariant |
L |
5.325568833849 |
L(r)(E,1)/r! |
Ω |
1.2829947199305 |
Real period |
R |
0.34590742730787 |
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 |
44688by1 33516s1 11172a1 |
Quadratic twists by: -4 -3 -7 |