Atkin-Lehner |
3+ 5- 23+ 61+ |
Signs for the Atkin-Lehner involutions |
Class |
21045a |
Isogeny class |
Conductor |
21045 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
3584 |
Modular degree for the optimal curve |
Δ |
-7891875 = -1 · 32 · 54 · 23 · 61 |
Discriminant |
Eigenvalues |
0 3+ 5- 1 -5 -5 -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,45,56] |
[a1,a2,a3,a4,a6] |
Generators |
[0:7:1] [6:22:1] |
Generators of the group modulo torsion |
j |
9855401984/7891875 |
j-invariant |
L |
5.781278186455 |
L(r)(E,1)/r! |
Ω |
1.5062589733381 |
Real period |
R |
0.47977126516648 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
63135f1 105225m1 |
Quadratic twists by: -3 5 |