Atkin-Lehner |
2- 3- 7- 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
42042dg |
Isogeny class |
Conductor |
42042 |
Conductor |
∏ cp |
144 |
Product of Tamagawa factors cp |
deg |
165888 |
Modular degree for the optimal curve |
Δ |
24187520028672 = 212 · 33 · 76 · 11 · 132 |
Discriminant |
Eigenvalues |
2- 3- -2 7- 11+ 13- -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-52284,-4599792] |
[a1,a2,a3,a4,a6] |
Generators |
[-132:144:1] |
Generators of the group modulo torsion |
j |
134351465835313/205590528 |
j-invariant |
L |
9.6642078168159 |
L(r)(E,1)/r! |
Ω |
0.31575280927446 |
Real period |
R |
0.85019106480936 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000007 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
126126dc1 858e1 |
Quadratic twists by: -3 -7 |