Atkin-Lehner |
2+ 3- 31- |
Signs for the Atkin-Lehner involutions |
Class |
69192w |
Isogeny class |
Conductor |
69192 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
49152 |
Modular degree for the optimal curve |
Δ |
-253314541296 = -1 · 24 · 312 · 313 |
Discriminant |
Eigenvalues |
2+ 3- -3 1 -2 -2 0 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,1581,-961] |
[a1,a2,a3,a4,a6] |
Generators |
[31:-279:1] |
Generators of the group modulo torsion |
j |
1257728/729 |
j-invariant |
L |
4.3283212804746 |
L(r)(E,1)/r! |
Ω |
0.5849200064403 |
Real period |
R |
0.92498145749189 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999997414 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
23064j1 69192v1 |
Quadratic twists by: -3 -31 |