Atkin-Lehner |
2+ 3+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
9024b |
Isogeny class |
Conductor |
9024 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1536 |
Modular degree for the optimal curve |
Δ |
-6930432 = -1 · 214 · 32 · 47 |
Discriminant |
Eigenvalues |
2+ 3+ 0 -4 4 -2 2 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,47,-47] |
[a1,a2,a3,a4,a6] |
Generators |
[7:24:1] |
Generators of the group modulo torsion |
j |
686000/423 |
j-invariant |
L |
3.2182768012352 |
L(r)(E,1)/r! |
Ω |
1.3656754237138 |
Real period |
R |
1.1782729429529 |
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 |
9024br1 1128f1 27072x1 |
Quadratic twists by: -4 8 -3 |