Atkin-Lehner |
2+ 3- 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696bw |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
18432 |
Modular degree for the optimal curve |
Δ |
-50808384 = -1 · 26 · 38 · 112 |
Discriminant |
Eigenvalues |
2+ 3- -1 -2 11- 1 5 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-363,-2684] |
[a1,a2,a3,a4,a6] |
Generators |
[716:19152:1] |
Generators of the group modulo torsion |
j |
-937024/9 |
j-invariant |
L |
6.0016821977269 |
L(r)(E,1)/r! |
Ω |
0.54656791011938 |
Real period |
R |
5.4903353150601 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999995215 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69696bt1 34848bu1 23232bs1 69696bu1 |
Quadratic twists by: -4 8 -3 -11 |