Atkin-Lehner |
2- 37+ 61- |
Signs for the Atkin-Lehner involutions |
Class |
36112g |
Isogeny class |
Conductor |
36112 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
21888 |
Modular degree for the optimal curve |
Δ |
-21891383296 = -1 · 218 · 372 · 61 |
Discriminant |
Eigenvalues |
2- 2 1 -1 3 1 0 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-4720,-123456] |
[a1,a2,a3,a4,a6] |
Generators |
[348990:2346614:3375] |
Generators of the group modulo torsion |
j |
-2839760855281/5344576 |
j-invariant |
L |
9.0747868052978 |
L(r)(E,1)/r! |
Ω |
0.28795684624411 |
Real period |
R |
7.8785996266997 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999999 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
4514c1 |
Quadratic twists by: -4 |