Atkin-Lehner |
2+ 3+ 23+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
4002b |
Isogeny class |
Conductor |
4002 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
7392 |
Modular degree for the optimal curve |
Δ |
-397480312836 = -1 · 22 · 311 · 23 · 293 |
Discriminant |
Eigenvalues |
2+ 3+ 1 4 -3 1 6 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-6612,-211932] |
[a1,a2,a3,a4,a6] |
j |
-31976054253232201/397480312836 |
j-invariant |
L |
1.5871122860468 |
L(r)(E,1)/r! |
Ω |
0.26451871434113 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
32016bg1 128064x1 12006q1 100050cn1 |
Quadratic twists by: -4 8 -3 5 |