Atkin-Lehner |
2+ 3- 31+ 59- |
Signs for the Atkin-Lehner involutions |
Class |
32922a |
Isogeny class |
Conductor |
32922 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
69888 |
Modular degree for the optimal curve |
Δ |
-594094082688 = -1 · 27 · 36 · 31 · 593 |
Discriminant |
Eigenvalues |
2+ 3- -4 0 0 2 -6 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-1869,48869] |
[a1,a2,a3,a4,a6] |
Generators |
[-35:283:1] |
Generators of the group modulo torsion |
j |
-990728800209/814943872 |
j-invariant |
L |
2.341866808083 |
L(r)(E,1)/r! |
Ω |
0.84058282001557 |
Real period |
R |
0.4643339423392 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000002 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
3658b1 |
Quadratic twists by: -3 |