Atkin-Lehner |
3- 7+ 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
9009d |
Isogeny class |
Conductor |
9009 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
3584 |
Modular degree for the optimal curve |
Δ |
-2252673423 = -1 · 38 · 74 · 11 · 13 |
Discriminant |
Eigenvalues |
-1 3- -2 7+ 11+ 13+ -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,94,-2280] |
[a1,a2,a3,a4,a6] |
Generators |
[14:33:1] [20:75:1] |
Generators of the group modulo torsion |
j |
127263527/3090087 |
j-invariant |
L |
3.5061573806272 |
L(r)(E,1)/r! |
Ω |
0.70685876201244 |
Real period |
R |
2.4800975591259 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999986 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
3003a1 63063p1 99099cb1 117117bq1 |
Quadratic twists by: -3 -7 -11 13 |