Atkin-Lehner |
2- 3+ 7+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
52416ec |
Isogeny class |
Conductor |
52416 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1013760 |
Modular degree for the optimal curve |
Δ |
-2308844685084327936 = -1 · 229 · 39 · 75 · 13 |
Discriminant |
Eigenvalues |
2- 3+ -3 7+ 1 13- 5 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-2159244,1223425296] |
[a1,a2,a3,a4,a6] |
Generators |
[-1566:27648:1] |
Generators of the group modulo torsion |
j |
-215773279370739/447469568 |
j-invariant |
L |
4.5074147556404 |
L(r)(E,1)/r! |
Ω |
0.25938966102557 |
Real period |
R |
2.1721252968679 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999188 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
52416bi1 13104bd1 52416ea1 |
Quadratic twists by: -4 8 -3 |