Atkin-Lehner |
2- 3- 13- 31- |
Signs for the Atkin-Lehner involutions |
Class |
38688f |
Isogeny class |
Conductor |
38688 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
11776 |
Modular degree for the optimal curve |
Δ |
-31182528 = -1 · 26 · 3 · 132 · 312 |
Discriminant |
Eigenvalues |
2- 3- -4 0 -2 13- 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-130,-676] |
[a1,a2,a3,a4,a6] |
Generators |
[130:1482:1] |
Generators of the group modulo torsion |
j |
-3825694144/487227 |
j-invariant |
L |
4.6176022111752 |
L(r)(E,1)/r! |
Ω |
0.7014976395474 |
Real period |
R |
3.2912457226178 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000003 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
38688d1 77376bc2 116064k1 |
Quadratic twists by: -4 8 -3 |