Atkin-Lehner |
2- 3+ 7+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
38976bb |
Isogeny class |
Conductor |
38976 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
196608 |
Modular degree for the optimal curve |
Δ |
-1183275858788352 = -1 · 218 · 33 · 78 · 29 |
Discriminant |
Eigenvalues |
2- 3+ 2 7+ 4 2 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-50177,-4615263] |
[a1,a2,a3,a4,a6] |
j |
-53297461115137/4513839183 |
j-invariant |
L |
2.8570504443169 |
L(r)(E,1)/r! |
Ω |
0.15872502468436 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
9 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
38976x1 9744q1 116928dw1 |
Quadratic twists by: -4 8 -3 |