Atkin-Lehner |
2- 13+ 103- |
Signs for the Atkin-Lehner involutions |
Class |
69628d |
Isogeny class |
Conductor |
69628 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
1693440 |
Modular degree for the optimal curve |
Δ |
7986210810624527104 = 28 · 1313 · 103 |
Discriminant |
Eigenvalues |
2- -1 -3 0 -2 13+ 7 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-6510612,-6390505304] |
[a1,a2,a3,a4,a6] |
Generators |
[-1938970:742586:1331] |
Generators of the group modulo torsion |
j |
24699555786200272/6463097251 |
j-invariant |
L |
3.1838883322708 |
L(r)(E,1)/r! |
Ω |
0.094515038404469 |
Real period |
R |
2.8072149385942 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999984321 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
5356b1 |
Quadratic twists by: 13 |