Atkin-Lehner |
2- 3+ 5- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
27840cy |
Isogeny class |
Conductor |
27840 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
18432 |
Modular degree for the optimal curve |
Δ |
21894266880 = 224 · 32 · 5 · 29 |
Discriminant |
Eigenvalues |
2- 3+ 5- 2 -2 0 -2 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-705,1377] |
[a1,a2,a3,a4,a6] |
Generators |
[27:36:1] |
Generators of the group modulo torsion |
j |
148035889/83520 |
j-invariant |
L |
4.9154733020999 |
L(r)(E,1)/r! |
Ω |
1.0408397913078 |
Real period |
R |
2.3613015870213 |
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 |
27840ca1 6960bi1 83520fe1 |
Quadratic twists by: -4 8 -3 |