Atkin-Lehner |
11+ 13+ 41+ |
Signs for the Atkin-Lehner involutions |
Class |
76219b |
Isogeny class |
Conductor |
76219 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
129168 |
Modular degree for the optimal curve |
Δ |
367894555171 = 11 · 138 · 41 |
Discriminant |
Eigenvalues |
-1 1 3 4 11+ 13+ -6 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-4989,-132874] |
[a1,a2,a3,a4,a6] |
Generators |
[-11757945:10039786:328509] |
Generators of the group modulo torsion |
j |
16835377/451 |
j-invariant |
L |
6.8340654805309 |
L(r)(E,1)/r! |
Ω |
0.56899169567591 |
Real period |
R |
12.01083518705 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001416 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
76219f1 |
Quadratic twists by: 13 |