Atkin-Lehner |
2+ 3- 7- 11- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
31878p |
Isogeny class |
Conductor |
31878 |
Conductor |
∏ cp |
168 |
Product of Tamagawa factors cp |
deg |
274176 |
Modular degree for the optimal curve |
Δ |
-1984922046202788 = -1 · 22 · 39 · 77 · 113 · 23 |
Discriminant |
Eigenvalues |
2+ 3- -4 7- 11- -1 -7 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-11394,2196904] |
[a1,a2,a3,a4,a6] |
Generators |
[92:-1432:1] [-139:1109:1] |
Generators of the group modulo torsion |
j |
-224412099736609/2722801160772 |
j-invariant |
L |
5.3383253912977 |
L(r)(E,1)/r! |
Ω |
0.39614305184379 |
Real period |
R |
0.080212807542309 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
10626n1 |
Quadratic twists by: -3 |