Atkin-Lehner |
3- 7+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
399c |
Isogeny class |
Conductor |
399 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
168 |
Modular degree for the optimal curve |
Δ |
1008273 = 3 · 72 · 193 |
Discriminant |
Eigenvalues |
-1 3- 4 7+ -2 4 0 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-431,3408] |
[a1,a2,a3,a4,a6] |
j |
8855610342769/1008273 |
j-invariant |
L |
1.3331183260701 |
L(r)(E,1)/r! |
Ω |
2.6662366521403 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
6384z1 25536l1 1197c1 9975d1 |
Quadratic twists by: -4 8 -3 5 |