Atkin-Lehner |
2- 3+ 23+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
24012a |
Isogeny class |
Conductor |
24012 |
Conductor |
∏ cp |
36 |
Product of Tamagawa factors cp |
deg |
23616 |
Modular degree for the optimal curve |
Δ |
-5573569392 = -1 · 24 · 33 · 232 · 293 |
Discriminant |
Eigenvalues |
2- 3+ 0 -1 3 5 3 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-17745,909841] |
[a1,a2,a3,a4,a6] |
Generators |
[77:3:1] |
Generators of the group modulo torsion |
j |
-1430434500768000/12901781 |
j-invariant |
L |
5.8472806332387 |
L(r)(E,1)/r! |
Ω |
1.2195020552064 |
Real period |
R |
1.1987024967024 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
96048r1 24012c2 |
Quadratic twists by: -4 -3 |