Atkin-Lehner |
2+ 3- 47- |
Signs for the Atkin-Lehner involutions |
Class |
6768f |
Isogeny class |
Conductor |
6768 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
2048 |
Modular degree for the optimal curve |
Δ |
-315767808 = -1 · 210 · 38 · 47 |
Discriminant |
Eigenvalues |
2+ 3- -2 0 -6 0 6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,69,826] |
[a1,a2,a3,a4,a6] |
Generators |
[5:36:1] |
Generators of the group modulo torsion |
j |
48668/423 |
j-invariant |
L |
3.3777216815049 |
L(r)(E,1)/r! |
Ω |
1.25823236751 |
Real period |
R |
0.67112438225328 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
3384b1 27072co1 2256d1 |
Quadratic twists by: -4 8 -3 |