Atkin-Lehner |
2- 3- 11+ |
Signs for the Atkin-Lehner involutions |
Class |
69696fc |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
168960 |
Modular degree for the optimal curve |
Δ |
110012407471296 = 26 · 36 · 119 |
Discriminant |
Eigenvalues |
2- 3- 2 0 11+ -4 8 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-11979,0] |
[a1,a2,a3,a4,a6] |
Generators |
[1090721700:64208316195:314432] |
Generators of the group modulo torsion |
j |
1728 |
j-invariant |
L |
7.7727297850811 |
L(r)(E,1)/r! |
Ω |
0.50126464554598 |
Real period |
R |
15.506239776172 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999066 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69696fc1 34848br2 7744p1 69696fb1 |
Quadratic twists by: -4 8 -3 -11 |