Atkin-Lehner |
2- 3+ 5+ 17+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
19380b |
Isogeny class |
Conductor |
19380 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
6144 |
Modular degree for the optimal curve |
Δ |
4418640 = 24 · 32 · 5 · 17 · 192 |
Discriminant |
Eigenvalues |
2- 3+ 5+ -4 -2 0 17+ 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-261,1710] |
[a1,a2,a3,a4,a6] |
Generators |
[-15:45:1] [-9:57:1] |
Generators of the group modulo torsion |
j |
123363917824/276165 |
j-invariant |
L |
5.543033751436 |
L(r)(E,1)/r! |
Ω |
2.4586083623213 |
Real period |
R |
0.7515137203068 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999993 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
77520cj1 58140p1 96900bb1 |
Quadratic twists by: -4 -3 5 |