Atkin-Lehner |
5- 7+ 13+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
21385i |
Isogeny class |
Conductor |
21385 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
2432 |
Modular degree for the optimal curve |
Δ |
-748475 = -1 · 52 · 72 · 13 · 47 |
Discriminant |
Eigenvalues |
0 -1 5- 7+ -3 13+ -1 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-105,453] |
[a1,a2,a3,a4,a6] |
Generators |
[-11:12:1] [7:3:1] |
Generators of the group modulo torsion |
j |
-129247215616/748475 |
j-invariant |
L |
5.4728660871243 |
L(r)(E,1)/r! |
Ω |
2.8602298559864 |
Real period |
R |
0.47835893990041 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999993 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
106925r1 |
Quadratic twists by: 5 |