Atkin-Lehner |
2- 5+ 13+ 41+ |
Signs for the Atkin-Lehner involutions |
Class |
69290p |
Isogeny class |
Conductor |
69290 |
Conductor |
∏ cp |
30 |
Product of Tamagawa factors cp |
deg |
97920 |
Modular degree for the optimal curve |
Δ |
-141905920000 = -1 · 215 · 54 · 132 · 41 |
Discriminant |
Eigenvalues |
2- -2 5+ -1 -4 13+ 2 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,159,18121] |
[a1,a2,a3,a4,a6] |
Generators |
[-24:37:1] [26:187:1] |
Generators of the group modulo torsion |
j |
2629406039/839680000 |
j-invariant |
L |
10.061616540732 |
L(r)(E,1)/r! |
Ω |
0.80138595162883 |
Real period |
R |
0.41850898102535 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000006 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69290n1 |
Quadratic twists by: 13 |