Atkin-Lehner |
2+ 19- 61- |
Signs for the Atkin-Lehner involutions |
Class |
2318b |
Isogeny class |
Conductor |
2318 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
192 |
Modular degree for the optimal curve |
Δ |
-141398 = -1 · 2 · 19 · 612 |
Discriminant |
Eigenvalues |
2+ -1 -2 1 0 -1 5 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,9,19] |
[a1,a2,a3,a4,a6] |
Generators |
[9:26:1] |
Generators of the group modulo torsion |
j |
67419143/141398 |
j-invariant |
L |
1.7408044777917 |
L(r)(E,1)/r! |
Ω |
2.2636990122303 |
Real period |
R |
0.38450440371853 |
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 |
18544g1 74176a1 20862z1 57950bp1 |
Quadratic twists by: -4 8 -3 5 |