Atkin-Lehner |
2- 3- 7- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
42042dn |
Isogeny class |
Conductor |
42042 |
Conductor |
∏ cp |
242 |
Product of Tamagawa factors cp |
deg |
139392 |
Modular degree for the optimal curve |
Δ |
-33047546628096 = -1 · 211 · 311 · 72 · 11 · 132 |
Discriminant |
Eigenvalues |
2- 3- -3 7- 11- 13+ -3 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-17837,956241] |
[a1,a2,a3,a4,a6] |
Generators |
[190:2011:1] |
Generators of the group modulo torsion |
j |
-12808391413763617/674439727104 |
j-invariant |
L |
8.6873636288852 |
L(r)(E,1)/r! |
Ω |
0.6482487303841 |
Real period |
R |
0.05537719571359 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000002 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
126126ca1 42042bx1 |
Quadratic twists by: -3 -7 |