Atkin-Lehner |
2- 3+ 7- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
42588c |
Isogeny class |
Conductor |
42588 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
193536 |
Modular degree for the optimal curve |
Δ |
-12587925780651312 = -1 · 24 · 39 · 72 · 138 |
Discriminant |
Eigenvalues |
2- 3+ 2 7- -2 13+ 4 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,54756,-2194803] |
[a1,a2,a3,a4,a6] |
Generators |
[2100020:44012501:8000] |
Generators of the group modulo torsion |
j |
11943936/8281 |
j-invariant |
L |
7.3882193539091 |
L(r)(E,1)/r! |
Ω |
0.22604207024091 |
Real period |
R |
8.171287922232 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000008 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
42588d1 3276b1 |
Quadratic twists by: -3 13 |