Atkin-Lehner |
2+ 17- 47- |
Signs for the Atkin-Lehner involutions |
Class |
12784b |
Isogeny class |
Conductor |
12784 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
3840 |
Modular degree for the optimal curve |
Δ |
-3477248 = -1 · 28 · 172 · 47 |
Discriminant |
Eigenvalues |
2+ 0 -4 -4 -6 6 17- 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-7,-90] |
[a1,a2,a3,a4,a6] |
Generators |
[9:24:1] |
Generators of the group modulo torsion |
j |
-148176/13583 |
j-invariant |
L |
1.9941949894037 |
L(r)(E,1)/r! |
Ω |
1.1067134595891 |
Real period |
R |
1.8019072345467 |
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 |
6392a1 51136o1 115056e1 |
Quadratic twists by: -4 8 -3 |