Atkin-Lehner |
2+ 3+ 7- 19- |
Signs for the Atkin-Lehner involutions |
Class |
3192d |
Isogeny class |
Conductor |
3192 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
9600 |
Modular degree for the optimal curve |
Δ |
333872185506048 = 28 · 35 · 710 · 19 |
Discriminant |
Eigenvalues |
2+ 3+ 0 7- 2 -4 0 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-23948,1131348] |
[a1,a2,a3,a4,a6] |
Generators |
[22:784:1] |
Generators of the group modulo torsion |
j |
5933482010818000/1304188224633 |
j-invariant |
L |
3.0164726048303 |
L(r)(E,1)/r! |
Ω |
0.51055778597355 |
Real period |
R |
1.181638078079 |
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 |
6384g1 25536bn1 9576ba1 79800bo1 |
Quadratic twists by: -4 8 -3 5 |