Atkin-Lehner |
2+ 3- 5- 11+ |
Signs for the Atkin-Lehner involutions |
Class |
31680bn |
Isogeny class |
Conductor |
31680 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
32768 |
Modular degree for the optimal curve |
Δ |
-46189440000 = -1 · 210 · 38 · 54 · 11 |
Discriminant |
Eigenvalues |
2+ 3- 5- -4 11+ -2 -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,888,-1784] |
[a1,a2,a3,a4,a6] |
Generators |
[17:135:1] |
Generators of the group modulo torsion |
j |
103737344/61875 |
j-invariant |
L |
4.3585786705272 |
L(r)(E,1)/r! |
Ω |
0.66233676592729 |
Real period |
R |
0.82257600943097 |
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 |
31680ed1 3960f1 10560x1 |
Quadratic twists by: -4 8 -3 |