Atkin-Lehner |
2+ 3- 7+ 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
78078x |
Isogeny class |
Conductor |
78078 |
Conductor |
∏ cp |
80 |
Product of Tamagawa factors cp |
deg |
184320 |
Modular degree for the optimal curve |
Δ |
-946674512784 = -1 · 24 · 310 · 72 · 112 · 132 |
Discriminant |
Eigenvalues |
2+ 3- -1 7+ 11+ 13+ -3 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-15019,708710] |
[a1,a2,a3,a4,a6] |
Generators |
[232:-3235:1] [-125:860:1] |
Generators of the group modulo torsion |
j |
-2216759056780801/5601624336 |
j-invariant |
L |
8.9490780828615 |
L(r)(E,1)/r! |
Ω |
0.8846322772505 |
Real period |
R |
0.12645194948603 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999263 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
78078dh1 |
Quadratic twists by: 13 |