Atkin-Lehner |
2+ 13+ 103+ |
Signs for the Atkin-Lehner involutions |
Class |
85696i |
Isogeny class |
Conductor |
85696 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
211968 |
Modular degree for the optimal curve |
Δ |
-289232912384 = -1 · 221 · 13 · 1032 |
Discriminant |
Eigenvalues |
2+ -3 -1 5 4 13+ -3 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,1652,1264] |
[a1,a2,a3,a4,a6] |
Generators |
[350:6592:1] |
Generators of the group modulo torsion |
j |
1902014919/1103336 |
j-invariant |
L |
4.6666727278524 |
L(r)(E,1)/r! |
Ω |
0.58529333287235 |
Real period |
R |
0.99665254581021 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000001249 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
85696bz1 2678c1 |
Quadratic twists by: -4 8 |