Atkin-Lehner |
2- 3+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
21312bj |
Isogeny class |
Conductor |
21312 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
24576 |
Modular degree for the optimal curve |
Δ |
-190911873024 = -1 · 218 · 39 · 37 |
Discriminant |
Eigenvalues |
2- 3+ 2 4 4 2 -6 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,756,-19440] |
[a1,a2,a3,a4,a6] |
Generators |
[40970:744128:125] |
Generators of the group modulo torsion |
j |
9261/37 |
j-invariant |
L |
7.1356529400232 |
L(r)(E,1)/r! |
Ω |
0.511011034936 |
Real period |
R |
6.981897113941 |
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 |
21312f1 5328j1 21312bn1 |
Quadratic twists by: -4 8 -3 |