Atkin-Lehner |
3- 19- 89- |
Signs for the Atkin-Lehner involutions |
Class |
15219i |
Isogeny class |
Conductor |
15219 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
9984 |
Modular degree for the optimal curve |
Δ |
-70266123 = -1 · 37 · 192 · 89 |
Discriminant |
Eigenvalues |
-2 3- -2 -4 0 -6 0 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-561,5130] |
[a1,a2,a3,a4,a6] |
Generators |
[-4:85:1] [5:49:1] |
Generators of the group modulo torsion |
j |
-26784575488/96387 |
j-invariant |
L |
2.9581959296127 |
L(r)(E,1)/r! |
Ω |
1.9570462628974 |
Real period |
R |
0.18894519675489 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
5073h1 |
Quadratic twists by: -3 |