Atkin-Lehner |
2- 3- 7- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
78078di |
Isogeny class |
Conductor |
78078 |
Conductor |
∏ cp |
96 |
Product of Tamagawa factors cp |
deg |
1806336 |
Modular degree for the optimal curve |
Δ |
-3202823329027366044 = -1 · 22 · 3 · 74 · 116 · 137 |
Discriminant |
Eigenvalues |
2- 3- 2 7- 11- 13+ -4 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,179728,-80940900] |
[a1,a2,a3,a4,a6] |
Generators |
[12324:258718:27] |
Generators of the group modulo torsion |
j |
133018079080823/663548801916 |
j-invariant |
L |
15.47371354556 |
L(r)(E,1)/r! |
Ω |
0.12681312948757 |
Real period |
R |
5.0841586120743 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999998457 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
6006j1 |
Quadratic twists by: 13 |