Atkin-Lehner |
3- 13- 103+ |
Signs for the Atkin-Lehner involutions |
Class |
52221j |
Isogeny class |
Conductor |
52221 |
Conductor |
∏ cp |
18 |
Product of Tamagawa factors cp |
deg |
39744 |
Modular degree for the optimal curve |
Δ |
-4454085753 = -1 · 39 · 133 · 103 |
Discriminant |
Eigenvalues |
-1 3- -2 1 5 13- -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-1934,32733] |
[a1,a2,a3,a4,a6] |
Generators |
[1:175:1] |
Generators of the group modulo torsion |
j |
-364147304221/2027349 |
j-invariant |
L |
4.1652649977531 |
L(r)(E,1)/r! |
Ω |
1.3862531389621 |
Real period |
R |
0.16692738467662 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999822 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
52221i1 |
Quadratic twists by: 13 |