Atkin-Lehner |
3+ 11+ 19- 53+ |
Signs for the Atkin-Lehner involutions |
Class |
33231a |
Isogeny class |
Conductor |
33231 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
16704 |
Modular degree for the optimal curve |
Δ |
2398314501 = 39 · 112 · 19 · 53 |
Discriminant |
Eigenvalues |
1 3+ -1 -1 11+ 2 -6 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-608,-5529] |
[a1,a2,a3,a4,a6] |
Generators |
[-130:223:8] [-14:29:1] |
Generators of the group modulo torsion |
j |
24920116376329/2398314501 |
j-invariant |
L |
8.1867283745671 |
L(r)(E,1)/r! |
Ω |
0.96717926536665 |
Real period |
R |
4.2322704113513 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999993 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
99693i1 |
Quadratic twists by: -3 |