Atkin-Lehner |
2- 7+ 19- 37+ |
Signs for the Atkin-Lehner involutions |
Class |
19684b |
Isogeny class |
Conductor |
19684 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
4224 |
Modular degree for the optimal curve |
Δ |
-23935744 = -1 · 28 · 7 · 192 · 37 |
Discriminant |
Eigenvalues |
2- 0 -1 7+ 5 -3 -2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-488,-4156] |
[a1,a2,a3,a4,a6] |
Generators |
[32:114:1] |
Generators of the group modulo torsion |
j |
-50204565504/93499 |
j-invariant |
L |
4.2805738961124 |
L(r)(E,1)/r! |
Ω |
0.50782740253969 |
Real period |
R |
1.4048650764364 |
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 |
78736s1 |
Quadratic twists by: -4 |