Atkin-Lehner |
2+ 3+ 13- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
72384q |
Isogeny class |
Conductor |
72384 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
18432 |
Modular degree for the optimal curve |
Δ |
100758528 = 210 · 32 · 13 · 292 |
Discriminant |
Eigenvalues |
2+ 3+ 2 2 0 13- 6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-117,117] |
[a1,a2,a3,a4,a6] |
j |
174456832/98397 |
j-invariant |
L |
3.2600077720805 |
L(r)(E,1)/r! |
Ω |
1.6300038819927 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
72384dm1 4524d1 |
Quadratic twists by: -4 8 |