Atkin-Lehner |
3- 5+ 13+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
49725i |
Isogeny class |
Conductor |
49725 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
131072 |
Modular degree for the optimal curve |
Δ |
294527390625 = 38 · 56 · 132 · 17 |
Discriminant |
Eigenvalues |
-1 3- 5+ 0 -4 13+ 17- -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-121280,-16226278] |
[a1,a2,a3,a4,a6] |
Generators |
[1024:30025:1] |
Generators of the group modulo torsion |
j |
17319700013617/25857 |
j-invariant |
L |
2.8147030485251 |
L(r)(E,1)/r! |
Ω |
0.25583065118025 |
Real period |
R |
5.5011059768619 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999319 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
16575f1 1989e1 |
Quadratic twists by: -3 5 |