Atkin-Lehner |
2+ 5- 11+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
78320p |
Isogeny class |
Conductor |
78320 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
32256 |
Modular degree for the optimal curve |
Δ |
-2788192000 = -1 · 28 · 53 · 11 · 892 |
Discriminant |
Eigenvalues |
2+ -2 5- 0 11+ -2 2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,340,-692] |
[a1,a2,a3,a4,a6] |
Generators |
[6:40:1] [27:170:1] |
Generators of the group modulo torsion |
j |
16929437744/10891375 |
j-invariant |
L |
8.1490957527904 |
L(r)(E,1)/r! |
Ω |
0.82076117246955 |
Real period |
R |
3.3095684129151 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999182 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
39160h1 |
Quadratic twists by: -4 |