Atkin-Lehner |
2+ 3- 7- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
49686be |
Isogeny class |
Conductor |
49686 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
978432 |
Modular degree for the optimal curve |
Δ |
18157617678415488 = 27 · 3 · 73 · 1310 |
Discriminant |
Eigenvalues |
2+ 3- 0 7- -5 13+ 3 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-2728171,-1734639658] |
[a1,a2,a3,a4,a6] |
Generators |
[-80138793787440:42555822833749:83855130633] |
Generators of the group modulo torsion |
j |
47490922375/384 |
j-invariant |
L |
4.812215401008 |
L(r)(E,1)/r! |
Ω |
0.11747133042921 |
Real period |
R |
20.482510002337 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
49686g2 49686cw1 |
Quadratic twists by: -7 13 |