Atkin-Lehner |
2+ 7- 13+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
68614g |
Isogeny class |
Conductor |
68614 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
981120 |
Modular degree for the optimal curve |
Δ |
-21100896479391638 = -1 · 2 · 7 · 1311 · 292 |
Discriminant |
Eigenvalues |
2+ -1 -2 7- 1 13+ -4 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-1246716,-536361314] |
[a1,a2,a3,a4,a6] |
Generators |
[7285:610419:1] |
Generators of the group modulo torsion |
j |
-44398340949270673/4371603782 |
j-invariant |
L |
1.8329565404385 |
L(r)(E,1)/r! |
Ω |
0.071437305419528 |
Real period |
R |
3.2072817717252 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002688 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
5278e1 |
Quadratic twists by: 13 |