Atkin-Lehner |
2- 3+ 13- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
20826u |
Isogeny class |
Conductor |
20826 |
Conductor |
∏ cp |
192 |
Product of Tamagawa factors cp |
deg |
165888 |
Modular degree for the optimal curve |
Δ |
-22674811687796736 = -1 · 232 · 33 · 133 · 89 |
Discriminant |
Eigenvalues |
2- 3+ 1 3 3 13- -8 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,56593,-5077257] |
[a1,a2,a3,a4,a6] |
Generators |
[947:29478:1] |
Generators of the group modulo torsion |
j |
742429622972858157/839807840288768 |
j-invariant |
L |
9.4186790694623 |
L(r)(E,1)/r! |
Ω |
0.20519623421094 |
Real period |
R |
0.23906686368825 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
20826f1 |
Quadratic twists by: -3 |