Atkin-Lehner |
2- 3- 13+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
69264s |
Isogeny class |
Conductor |
69264 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
345600 |
Modular degree for the optimal curve |
Δ |
-9968096541192192 = -1 · 212 · 311 · 135 · 37 |
Discriminant |
Eigenvalues |
2- 3- 0 -4 3 13+ -1 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-48000,6281584] |
[a1,a2,a3,a4,a6] |
j |
-4096000000000/3338295363 |
j-invariant |
L |
0.7476202019041 |
L(r)(E,1)/r! |
Ω |
0.37381010286234 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
4329b1 23088o1 |
Quadratic twists by: -4 -3 |