Atkin-Lehner |
2+ 5+ 7+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
69440g |
Isogeny class |
Conductor |
69440 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
165888 |
Modular degree for the optimal curve |
Δ |
-51717176000 = -1 · 26 · 53 · 7 · 314 |
Discriminant |
Eigenvalues |
2+ -3 5+ 7+ -1 -7 -7 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-3328,-74702] |
[a1,a2,a3,a4,a6] |
Generators |
[111:961:1] |
Generators of the group modulo torsion |
j |
-63693291257856/808080875 |
j-invariant |
L |
0.96630530350347 |
L(r)(E,1)/r! |
Ω |
0.31404780165398 |
Real period |
R |
1.5384685053844 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999942436 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69440cy1 1085d1 |
Quadratic twists by: -4 8 |