Atkin-Lehner |
2+ 3- 31- |
Signs for the Atkin-Lehner involutions |
Class |
69192s |
Isogeny class |
Conductor |
69192 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1105920 |
Modular degree for the optimal curve |
Δ |
-1109055044703873024 = -1 · 211 · 39 · 317 |
Discriminant |
Eigenvalues |
2+ 3- 3 2 -5 -1 1 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-279651,-76205378] |
[a1,a2,a3,a4,a6] |
Generators |
[3281938:158752926:1331] |
Generators of the group modulo torsion |
j |
-1825346/837 |
j-invariant |
L |
8.7803177134583 |
L(r)(E,1)/r! |
Ω |
0.10156065273188 |
Real period |
R |
10.806741436215 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000143 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
23064p1 2232d1 |
Quadratic twists by: -3 -31 |