Atkin-Lehner |
2+ 3- 7+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
67032k |
Isogeny class |
Conductor |
67032 |
Conductor |
∏ cp |
60 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
-69343806185136 = -1 · 24 · 36 · 74 · 195 |
Discriminant |
Eigenvalues |
2+ 3- 1 7+ 1 2 2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-33222,-2364887] |
[a1,a2,a3,a4,a6] |
Generators |
[224:1197:1] |
Generators of the group modulo torsion |
j |
-144797599744/2476099 |
j-invariant |
L |
7.4162986911622 |
L(r)(E,1)/r! |
Ω |
0.17663317072653 |
Real period |
R |
0.69978349866148 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999996241 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
7448n1 67032t1 |
Quadratic twists by: -3 -7 |