Atkin-Lehner |
2- 3+ 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696eh |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
368640 |
Modular degree for the optimal curve |
Δ |
6284345127616512 = 214 · 39 · 117 |
Discriminant |
Eigenvalues |
2- 3+ 0 -2 11- -6 -6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-65340,-5174928] |
[a1,a2,a3,a4,a6] |
Generators |
[-171:999:1] |
Generators of the group modulo torsion |
j |
54000/11 |
j-invariant |
L |
4.549212335436 |
L(r)(E,1)/r! |
Ω |
0.3028802975675 |
Real period |
R |
3.7549589488047 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000803 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69696j1 17424f1 69696eg1 6336bh1 |
Quadratic twists by: -4 8 -3 -11 |