Atkin-Lehner |
3+ 5- 23+ 61+ |
Signs for the Atkin-Lehner involutions |
Class |
21045c |
Isogeny class |
Conductor |
21045 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
10752 |
Modular degree for the optimal curve |
Δ |
-25569675 = -1 · 36 · 52 · 23 · 61 |
Discriminant |
Eigenvalues |
-2 3+ 5- -1 -1 -3 -6 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-570,5438] |
[a1,a2,a3,a4,a6] |
Generators |
[-1:77:1] [12:13:1] |
Generators of the group modulo torsion |
j |
-20516816613376/25569675 |
j-invariant |
L |
3.5626495881689 |
L(r)(E,1)/r! |
Ω |
2.1138539768177 |
Real period |
R |
0.42134528061528 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000003 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
63135h1 105225n1 |
Quadratic twists by: -3 5 |