Atkin-Lehner |
2- 3- 7+ 11+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
47124i |
Isogeny class |
Conductor |
47124 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
69888 |
Modular degree for the optimal curve |
Δ |
-567655515504 = -1 · 24 · 313 · 7 · 11 · 172 |
Discriminant |
Eigenvalues |
2- 3- -1 7+ 11+ -5 17+ 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-11973,-505559] |
[a1,a2,a3,a4,a6] |
Generators |
[128:243:1] |
Generators of the group modulo torsion |
j |
-16273656645376/48667311 |
j-invariant |
L |
4.0743880757576 |
L(r)(E,1)/r! |
Ω |
0.22816080135615 |
Real period |
R |
2.2321910969887 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000013 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
15708f1 |
Quadratic twists by: -3 |