Atkin-Lehner |
3- 5+ 7- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
69825bs |
Isogeny class |
Conductor |
69825 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
32768 |
Modular degree for the optimal curve |
Δ |
-305484375 = -1 · 3 · 56 · 73 · 19 |
Discriminant |
Eigenvalues |
1 3- 5+ 7- -6 6 2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,149,473] |
[a1,a2,a3,a4,a6] |
Generators |
[33:187:1] |
Generators of the group modulo torsion |
j |
68921/57 |
j-invariant |
L |
8.25653417749 |
L(r)(E,1)/r! |
Ω |
1.1147466802147 |
Real period |
R |
3.7033230614303 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000613 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
2793a1 69825r1 |
Quadratic twists by: 5 -7 |