Atkin-Lehner |
2+ 3+ 29- 53- |
Signs for the Atkin-Lehner involutions |
Class |
9222c |
Isogeny class |
Conductor |
9222 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
50688 |
Modular degree for the optimal curve |
Δ |
175859115800832 = 28 · 312 · 293 · 53 |
Discriminant |
Eigenvalues |
2+ 3+ -2 4 2 2 6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-23041,-1195019] |
[a1,a2,a3,a4,a6] |
Generators |
[-111:157:1] |
Generators of the group modulo torsion |
j |
1352873328206581657/175859115800832 |
j-invariant |
L |
2.9688165634595 |
L(r)(E,1)/r! |
Ω |
0.39082129364843 |
Real period |
R |
2.5321177152732 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
73776w1 27666i1 |
Quadratic twists by: -4 -3 |