Atkin-Lehner |
2+ 3- 13+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
69966r |
Isogeny class |
Conductor |
69966 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
147456 |
Modular degree for the optimal curve |
Δ |
-2913519834108 = -1 · 22 · 38 · 136 · 23 |
Discriminant |
Eigenvalues |
2+ 3- -2 2 -6 13+ 0 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-2313,-92039] |
[a1,a2,a3,a4,a6] |
Generators |
[140:-1591:1] |
Generators of the group modulo torsion |
j |
-389017/828 |
j-invariant |
L |
2.9488947986478 |
L(r)(E,1)/r! |
Ω |
0.32265746834395 |
Real period |
R |
1.1424246639801 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999993891 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
23322l1 414b1 |
Quadratic twists by: -3 13 |