Atkin-Lehner |
2+ 3+ 43+ |
Signs for the Atkin-Lehner involutions |
Class |
24768d |
Isogeny class |
Conductor |
24768 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
36864 |
Modular degree for the optimal curve |
Δ |
-9003866259456 = -1 · 222 · 33 · 433 |
Discriminant |
Eigenvalues |
2+ 3+ -3 -1 -3 1 6 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,3636,-117136] |
[a1,a2,a3,a4,a6] |
Generators |
[46:384:1] |
Generators of the group modulo torsion |
j |
751089429/1272112 |
j-invariant |
L |
3.6716917295657 |
L(r)(E,1)/r! |
Ω |
0.38449275879521 |
Real period |
R |
1.1936803898046 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
24768bv1 774a1 24768c2 |
Quadratic twists by: -4 8 -3 |