Atkin-Lehner |
2- 7- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
69776p |
Isogeny class |
Conductor |
69776 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
221184 |
Modular degree for the optimal curve |
Δ |
8406094462976 = 214 · 78 · 89 |
Discriminant |
Eigenvalues |
2- 2 2 7- 0 4 6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-71752,-7372560] |
[a1,a2,a3,a4,a6] |
Generators |
[-215108799615705:-9167467645070:1409071586931] |
Generators of the group modulo torsion |
j |
84778086457/17444 |
j-invariant |
L |
11.889117198542 |
L(r)(E,1)/r! |
Ω |
0.29170636795274 |
Real period |
R |
20.378569864097 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000243 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
8722h1 9968j1 |
Quadratic twists by: -4 -7 |