Atkin-Lehner |
2+ 23+ 59+ |
Signs for the Atkin-Lehner involutions |
Class |
21712a |
Isogeny class |
Conductor |
21712 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
6912 |
Modular degree for the optimal curve |
Δ |
-677653232 = -1 · 24 · 233 · 592 |
Discriminant |
Eigenvalues |
2+ 1 2 2 -4 5 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,168,-877] |
[a1,a2,a3,a4,a6] |
Generators |
[1082:12685:8] |
Generators of the group modulo torsion |
j |
32579462912/42353327 |
j-invariant |
L |
7.4165084716833 |
L(r)(E,1)/r! |
Ω |
0.86131028221097 |
Real period |
R |
4.3053639465706 |
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 |
10856b1 86848u1 |
Quadratic twists by: -4 8 |