Atkin-Lehner |
2+ 7- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
21056k |
Isogeny class |
Conductor |
21056 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
9216 |
Modular degree for the optimal curve |
Δ |
-16904093696 = -1 · 220 · 73 · 47 |
Discriminant |
Eigenvalues |
2+ -1 -3 7- -3 -2 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,223,6049] |
[a1,a2,a3,a4,a6] |
Generators |
[-13:28:1] [-7:64:1] |
Generators of the group modulo torsion |
j |
4657463/64484 |
j-invariant |
L |
5.4359577199847 |
L(r)(E,1)/r! |
Ω |
0.91416363843834 |
Real period |
R |
0.49553105988696 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999983 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
21056q1 658c1 |
Quadratic twists by: -4 8 |