Atkin-Lehner |
2+ 3- 7+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
52416by |
Isogeny class |
Conductor |
52416 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
583680 |
Modular degree for the optimal curve |
Δ |
-2526519737034768384 = -1 · 215 · 325 · 7 · 13 |
Discriminant |
Eigenvalues |
2+ 3- -1 7+ 1 13- 5 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-457068,-141402224] |
[a1,a2,a3,a4,a6] |
Generators |
[111614272:7462140228:24389] |
Generators of the group modulo torsion |
j |
-442067613591752/105765793497 |
j-invariant |
L |
5.9744929894145 |
L(r)(E,1)/r! |
Ω |
0.090659669833602 |
Real period |
R |
8.2375286062095 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999063 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
52416cw1 26208h1 17472z1 |
Quadratic twists by: -4 8 -3 |