Atkin-Lehner |
2+ 3- 11+ 61+ |
Signs for the Atkin-Lehner involutions |
Class |
12078g |
Isogeny class |
Conductor |
12078 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
5632 |
Modular degree for the optimal curve |
Δ |
-1127022336 = -1 · 28 · 38 · 11 · 61 |
Discriminant |
Eigenvalues |
2+ 3- -2 0 11+ -2 -6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-18,1620] |
[a1,a2,a3,a4,a6] |
Generators |
[-9:36:1] [-3:42:1] |
Generators of the group modulo torsion |
j |
-912673/1545984 |
j-invariant |
L |
4.4340046414144 |
L(r)(E,1)/r! |
Ω |
1.2446915342737 |
Real period |
R |
1.7811660637678 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999991 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
96624bq1 4026j1 |
Quadratic twists by: -4 -3 |