Atkin-Lehner |
2+ 13- 17- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
8398d |
Isogeny class |
Conductor |
8398 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1024 |
Modular degree for the optimal curve |
Δ |
4148612 = 22 · 132 · 17 · 192 |
Discriminant |
Eigenvalues |
2+ 0 0 0 -2 13- 17- 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-47,89] |
[a1,a2,a3,a4,a6] |
Generators |
[1:6:1] |
Generators of the group modulo torsion |
j |
11619959625/4148612 |
j-invariant |
L |
2.8624165213729 |
L(r)(E,1)/r! |
Ω |
2.2612113773683 |
Real period |
R |
0.63293873142994 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
67184w1 75582bk1 109174o1 |
Quadratic twists by: -4 -3 13 |