Atkin-Lehner |
2- 19+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
57152n |
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] |
Generators |
[3429:188:1] |
Generators of the group modulo torsion |
j |
-18471699048587981865409/1408313065472 |
j-invariant |
L |
2.1064633522543 |
L(r)(E,1)/r! |
Ω |
0.22974436655517 |
Real period |
R |
2.2921817233058 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000254 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
57152b1 14288e1 |
Quadratic twists by: -4 8 |