Atkin-Lehner |
2+ 3- 7- |
Signs for the Atkin-Lehner involutions |
Class |
28224cu |
Isogeny class |
Conductor |
28224 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
73728 |
Modular degree for the optimal curve |
Δ |
-12910202661888 = -1 · 210 · 37 · 78 |
Discriminant |
Eigenvalues |
2+ 3- -4 7- 2 -6 -4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-2352,-178360] |
[a1,a2,a3,a4,a6] |
Generators |
[154:1764:1] |
Generators of the group modulo torsion |
j |
-16384/147 |
j-invariant |
L |
3.0117753601126 |
L(r)(E,1)/r! |
Ω |
0.30010828098894 |
Real period |
R |
1.2544536217844 |
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 |
28224gp1 1764k1 9408r1 4032j1 |
Quadratic twists by: -4 8 -3 -7 |