Atkin-Lehner |
2- 3+ 13- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
72384ch |
Isogeny class |
Conductor |
72384 |
Conductor |
∏ cp |
6 |
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 |
[150550729:88619752:103823] |
Generators of the group modulo torsion |
j |
-13210433346558574664/11286566811 |
j-invariant |
L |
5.2476766781275 |
L(r)(E,1)/r! |
Ω |
0.067372489621044 |
Real period |
R |
12.981749442299 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001414 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
72384dp1 36192n1 |
Quadratic twists by: -4 8 |