Atkin-Lehner |
2- 3- 37+ |
Signs for the Atkin-Lehner involutions |
Class |
21312bp |
Isogeny class |
Conductor |
21312 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
18432 |
Modular degree for the optimal curve |
Δ |
-1527294984192 = -1 · 221 · 39 · 37 |
Discriminant |
Eigenvalues |
2- 3- 0 1 -3 1 3 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,1140,-57584] |
[a1,a2,a3,a4,a6] |
Generators |
[32:108:1] |
Generators of the group modulo torsion |
j |
857375/7992 |
j-invariant |
L |
5.1277163811042 |
L(r)(E,1)/r! |
Ω |
0.41906598718763 |
Real period |
R |
1.5295074456879 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
21312j1 5328t1 7104u1 |
Quadratic twists by: -4 8 -3 |