Atkin-Lehner |
2+ 23+ 61- |
Signs for the Atkin-Lehner involutions |
Class |
22448a |
Isogeny class |
Conductor |
22448 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
3072 |
Modular degree for the optimal curve |
Δ |
-1369328 = -1 · 24 · 23 · 612 |
Discriminant |
Eigenvalues |
2+ 1 -2 2 -6 -5 -6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-4,55] |
[a1,a2,a3,a4,a6] |
Generators |
[-3:7:1] [45:305:1] |
Generators of the group modulo torsion |
j |
-562432/85583 |
j-invariant |
L |
7.8962508133174 |
L(r)(E,1)/r! |
Ω |
2.2135444747922 |
Real period |
R |
1.7836214504027 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999976 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
11224a1 89792j1 |
Quadratic twists by: -4 8 |