Atkin-Lehner |
2+ 3- 13+ 23+ |
Signs for the Atkin-Lehner involutions |
Class |
57408z |
Isogeny class |
Conductor |
57408 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
24576 |
Modular degree for the optimal curve |
Δ |
-5158453248 = -1 · 214 · 34 · 132 · 23 |
Discriminant |
Eigenvalues |
2+ 3- 0 -2 -2 13+ -2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-593,6351] |
[a1,a2,a3,a4,a6] |
Generators |
[-11:108:1] [-5:96:1] |
Generators of the group modulo torsion |
j |
-1409938000/314847 |
j-invariant |
L |
11.141851720878 |
L(r)(E,1)/r! |
Ω |
1.3013782767938 |
Real period |
R |
1.0701972592792 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999969 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
57408cd1 7176k1 |
Quadratic twists by: -4 8 |