Atkin-Lehner |
2+ 5- 7- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82810bj |
Isogeny class |
Conductor |
82810 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
707616 |
Modular degree for the optimal curve |
Δ |
-3838796143797160 = -1 · 23 · 5 · 76 · 138 |
Discriminant |
Eigenvalues |
2+ 2 5- 7- 3 13+ 6 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-82982,-9706276] |
[a1,a2,a3,a4,a6] |
Generators |
[49185897176860832553637175666109885665:1440593383569576636857083080888347974358:50148013774166229400315220269914839] |
Generators of the group modulo torsion |
j |
-658489/40 |
j-invariant |
L |
8.4530444259179 |
L(r)(E,1)/r! |
Ω |
0.14015145061887 |
Real period |
R |
60.313642053589 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
1690c1 82810cc1 |
Quadratic twists by: -7 13 |