Atkin-Lehner |
2- 3+ 23+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
24012b |
Isogeny class |
Conductor |
24012 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
123840 |
Modular degree for the optimal curve |
Δ |
-940520867533056 = -1 · 28 · 39 · 235 · 29 |
Discriminant |
Eigenvalues |
2- 3+ 1 -4 3 -5 0 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-113967,14882022] |
[a1,a2,a3,a4,a6] |
Generators |
[642:14364:1] |
Generators of the group modulo torsion |
j |
-32488510691952/186653947 |
j-invariant |
L |
4.7634882867851 |
L(r)(E,1)/r! |
Ω |
0.4990377148161 |
Real period |
R |
4.7726736330344 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
96048s1 24012d1 |
Quadratic twists by: -4 -3 |