Atkin-Lehner |
2- 3+ 7+ 13- 17- |
Signs for the Atkin-Lehner involutions |
Class |
111384bl |
Isogeny class |
Conductor |
111384 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
384000 |
Modular degree for the optimal curve |
Δ |
40690898001936 = 24 · 39 · 7 · 13 · 175 |
Discriminant |
Eigenvalues |
2- 3+ -1 7+ -6 13- 17- -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-56943,5221071] |
[a1,a2,a3,a4,a6] |
Generators |
[201:1377:1] [66:1323:1] |
Generators of the group modulo torsion |
j |
64838576072448/129206987 |
j-invariant |
L |
10.526289811636 |
L(r)(E,1)/r! |
Ω |
0.64564639141033 |
Real period |
R |
0.81517452529256 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999991834 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
111384b1 |
Quadratic twists by: -3 |