Atkin-Lehner |
2- 3- 5- 11- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
68970cs |
Isogeny class |
Conductor |
68970 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
185856 |
Modular degree for the optimal curve |
Δ |
-16494915892950 = -1 · 2 · 34 · 52 · 118 · 19 |
Discriminant |
Eigenvalues |
2- 3- 5- 1 11- -3 1 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-6960,-297450] |
[a1,a2,a3,a4,a6] |
Generators |
[13140:162015:64] |
Generators of the group modulo torsion |
j |
-173945761/76950 |
j-invariant |
L |
13.696039402313 |
L(r)(E,1)/r! |
Ω |
0.25585888648977 |
Real period |
R |
6.6912075976443 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000491 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68970bf1 |
Quadratic twists by: -11 |