Atkin-Lehner |
2+ 19- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
57152b |
Isogeny class |
Conductor |
57152 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
4070400 |
Modular degree for the optimal curve |
Δ |
-369180820235091968 = -1 · 243 · 19 · 472 |
Discriminant |
Eigenvalues |
2+ -1 -4 1 4 -5 -5 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-35245825,-80527888639] |
[a1,a2,a3,a4,a6] |
j |
-18471699048587981865409/1408313065472 |
j-invariant |
L |
1.1153088211912 |
L(r)(E,1)/r! |
Ω |
0.030980800552566 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
9 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
57152n1 1786d1 |
Quadratic twists by: -4 8 |