Atkin-Lehner |
3- 7+ 11+ 101- |
Signs for the Atkin-Lehner involutions |
Class |
69993d |
Isogeny class |
Conductor |
69993 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
Δ |
5841222489333 = 36 · 7 · 11 · 1014 |
Discriminant |
Eigenvalues |
-1 3- 2 7+ 11+ 2 2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-5609,-110924] |
[a1,a2,a3,a4,a6] |
Generators |
[-55:197:1] |
Generators of the group modulo torsion |
j |
26765780551497/8012650877 |
j-invariant |
L |
4.8593880347405 |
L(r)(E,1)/r! |
Ω |
0.56443663480484 |
Real period |
R |
4.3046355735588 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000698 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
7777b4 |
Quadratic twists by: -3 |