Atkin-Lehner |
2+ 5- 7+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
69440bj |
Isogeny class |
Conductor |
69440 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
40960 |
Modular degree for the optimal curve |
Δ |
-3888640000 = -1 · 212 · 54 · 72 · 31 |
Discriminant |
Eigenvalues |
2+ -2 5- 7+ 0 -2 -4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-425,4375] |
[a1,a2,a3,a4,a6] |
Generators |
[-7:84:1] [-5:80:1] |
Generators of the group modulo torsion |
j |
-2077552576/949375 |
j-invariant |
L |
7.56762499611 |
L(r)(E,1)/r! |
Ω |
1.3032505926603 |
Real period |
R |
0.72584131543753 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999205 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69440by1 34720b1 |
Quadratic twists by: -4 8 |