Atkin-Lehner |
2- 23+ 59- |
Signs for the Atkin-Lehner involutions |
Class |
21712g |
Isogeny class |
Conductor |
21712 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
9216 |
Modular degree for the optimal curve |
Δ |
-32727105536 = -1 · 220 · 232 · 59 |
Discriminant |
Eigenvalues |
2- -1 1 3 0 -4 -2 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,800,-256] |
[a1,a2,a3,a4,a6] |
Generators |
[16:128:1] |
Generators of the group modulo torsion |
j |
13806727199/7990016 |
j-invariant |
L |
4.7728764461722 |
L(r)(E,1)/r! |
Ω |
0.69742841595336 |
Real period |
R |
0.85544199537092 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
2714c1 86848q1 |
Quadratic twists by: -4 8 |