Atkin-Lehner |
2- 5+ 13+ 41- |
Signs for the Atkin-Lehner involutions |
Class |
69290q |
Isogeny class |
Conductor |
69290 |
Conductor |
∏ cp |
42 |
Product of Tamagawa factors cp |
deg |
733824 |
Modular degree for the optimal curve |
Δ |
-21939893472016000 = -1 · 27 · 53 · 138 · 412 |
Discriminant |
Eigenvalues |
2- 0 5+ 1 3 13+ -2 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-691918,221816157] |
[a1,a2,a3,a4,a6] |
Generators |
[465:-909:1] |
Generators of the group modulo torsion |
j |
-44909703885969/26896000 |
j-invariant |
L |
9.2991561416443 |
L(r)(E,1)/r! |
Ω |
0.37748110332877 |
Real period |
R |
0.58654188938737 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000383 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69290f1 |
Quadratic twists by: 13 |