Atkin-Lehner |
2- 3- 13- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
72384dp |
Isogeny class |
Conductor |
72384 |
Conductor |
∏ cp |
132 |
Product of Tamagawa factors cp |
deg |
760320 |
Modular degree for the optimal curve |
Δ |
-369838221262848 = -1 · 215 · 311 · 133 · 29 |
Discriminant |
Eigenvalues |
2- 3- -2 -2 -3 13- -3 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-1575969,760974975] |
[a1,a2,a3,a4,a6] |
Generators |
[-1293:25272:1] [813:-4212:1] |
Generators of the group modulo torsion |
j |
-13210433346558574664/11286566811 |
j-invariant |
L |
10.562397730603 |
L(r)(E,1)/r! |
Ω |
0.44779263725211 |
Real period |
R |
0.17869468581914 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999859 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
72384ch1 36192e1 |
Quadratic twists by: -4 8 |