Atkin-Lehner |
2+ 3+ 7- 13- |
Signs for the Atkin-Lehner involutions |
Class |
49686x |
Isogeny class |
Conductor |
49686 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
576000 |
Modular degree for the optimal curve |
Δ |
-14069303198496 = -1 · 25 · 35 · 77 · 133 |
Discriminant |
Eigenvalues |
2+ 3+ -3 7- -5 13- 3 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-577294,168587476] |
[a1,a2,a3,a4,a6] |
Generators |
[447:95:1] |
Generators of the group modulo torsion |
j |
-82318551880501/54432 |
j-invariant |
L |
2.0514424032776 |
L(r)(E,1)/r! |
Ω |
0.58265546060476 |
Real period |
R |
0.88021246773753 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999948 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
7098p1 49686cr1 |
Quadratic twists by: -7 13 |