Atkin-Lehner |
2- 3- 7+ 59+ |
Signs for the Atkin-Lehner involutions |
Class |
69384x |
Isogeny class |
Conductor |
69384 |
Conductor |
∏ cp |
84 |
Product of Tamagawa factors cp |
deg |
865536 |
Modular degree for the optimal curve |
Δ |
-1665842180071394304 = -1 · 210 · 314 · 78 · 59 |
Discriminant |
Eigenvalues |
2- 3- -1 7+ 0 0 -1 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-958456,366145856] |
[a1,a2,a3,a4,a6] |
Generators |
[800:10584:1] |
Generators of the group modulo torsion |
j |
-16495156100836/282195171 |
j-invariant |
L |
6.9329623594296 |
L(r)(E,1)/r! |
Ω |
0.26657950128634 |
Real period |
R |
0.3096084499389 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000598 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69384v1 |
Quadratic twists by: -7 |