Atkin-Lehner |
2- 3- 7- 79- |
Signs for the Atkin-Lehner involutions |
Class |
69678bk |
Isogeny class |
Conductor |
69678 |
Conductor |
∏ cp |
128 |
Product of Tamagawa factors cp |
deg |
1769472 |
Modular degree for the optimal curve |
Δ |
-6293293611274559232 = -1 · 28 · 314 · 77 · 792 |
Discriminant |
Eigenvalues |
2- 3- 2 7- 0 -6 8 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,236146,112265885] |
[a1,a2,a3,a4,a6] |
Generators |
[-75:9739:1] |
Generators of the group modulo torsion |
j |
16980538103927/73377384192 |
j-invariant |
L |
11.270241057404 |
L(r)(E,1)/r! |
Ω |
0.17039975733603 |
Real period |
R |
2.0668752030552 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999837 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
23226q1 9954d1 |
Quadratic twists by: -3 -7 |