Atkin-Lehner |
2- 5+ 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
57200z |
Isogeny class |
Conductor |
57200 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
129024 |
Modular degree for the optimal curve |
Δ |
-76144640000000 = -1 · 219 · 57 · 11 · 132 |
Discriminant |
Eigenvalues |
2- -1 5+ -1 11+ 13+ -5 -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,10592,-18688] |
[a1,a2,a3,a4,a6] |
Generators |
[112:1600:1] [37:650:1] |
Generators of the group modulo torsion |
j |
2053225511/1189760 |
j-invariant |
L |
7.9173122040057 |
L(r)(E,1)/r! |
Ω |
0.36375001573526 |
Real period |
R |
0.68018143140238 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999892 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
7150t1 11440h1 |
Quadratic twists by: -4 5 |