Atkin-Lehner |
3- 23- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
49197k |
Isogeny class |
Conductor |
49197 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
684288 |
Modular degree for the optimal curve |
Δ |
76945650276753 = 36 · 237 · 31 |
Discriminant |
Eigenvalues |
-1 3- 2 0 4 -2 -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-5728552,-5277821377] |
[a1,a2,a3,a4,a6] |
Generators |
[-151843405043639861:75682202397526858:109881590603273] |
Generators of the group modulo torsion |
j |
140440148435570257/519777 |
j-invariant |
L |
5.8275591723187 |
L(r)(E,1)/r! |
Ω |
0.09758618483845 |
Real period |
R |
19.905683650939 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000051 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
2139c1 |
Quadratic twists by: -23 |