Atkin-Lehner |
3- 7- 11+ 43- |
Signs for the Atkin-Lehner involutions |
Class |
69531l |
Isogeny class |
Conductor |
69531 |
Conductor |
∏ cp |
128 |
Product of Tamagawa factors cp |
deg |
491520 |
Modular degree for the optimal curve |
Δ |
-27595005922673343 = -1 · 34 · 77 · 112 · 434 |
Discriminant |
Eigenvalues |
-1 3- -2 7- 11+ 2 -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,39836,-7379905] |
[a1,a2,a3,a4,a6] |
Generators |
[137:740:1] [2174:37721:8] |
Generators of the group modulo torsion |
j |
59424010905167/234553680207 |
j-invariant |
L |
7.2364069900682 |
L(r)(E,1)/r! |
Ω |
0.18993899643292 |
Real period |
R |
4.7623231181987 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999841 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
9933a1 |
Quadratic twists by: -7 |