Atkin-Lehner |
2+ 3- 19- |
Signs for the Atkin-Lehner involutions |
Class |
51984y |
Isogeny class |
Conductor |
51984 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
13824 |
Modular degree for the optimal curve |
Δ |
-113689008 = -1 · 24 · 39 · 192 |
Discriminant |
Eigenvalues |
2+ 3- -2 3 0 -5 4 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,114,-209] |
[a1,a2,a3,a4,a6] |
Generators |
[35:216:1] |
Generators of the group modulo torsion |
j |
38912/27 |
j-invariant |
L |
5.517818250832 |
L(r)(E,1)/r! |
Ω |
1.0580139474875 |
Real period |
R |
2.6076302037168 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999783 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
25992l1 17328n1 51984m1 |
Quadratic twists by: -4 -3 -19 |