Atkin-Lehner |
2- 3+ 11- 41+ |
Signs for the Atkin-Lehner involutions |
Class |
21648r |
Isogeny class |
Conductor |
21648 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
82944 |
Modular degree for the optimal curve |
Δ |
536073121824768 = 230 · 33 · 11 · 412 |
Discriminant |
Eigenvalues |
2- 3+ 0 2 11- 0 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-163688,25520496] |
[a1,a2,a3,a4,a6] |
Generators |
[130:2534:1] |
Generators of the group modulo torsion |
j |
118417788018699625/130877227008 |
j-invariant |
L |
4.8744813893917 |
L(r)(E,1)/r! |
Ω |
0.51811803137233 |
Real period |
R |
4.7040260078198 |
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 |
2706d1 86592cq1 64944bd1 |
Quadratic twists by: -4 8 -3 |