Atkin-Lehner |
2- 3+ 61+ |
Signs for the Atkin-Lehner involutions |
Class |
11712q |
Isogeny class |
Conductor |
11712 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
3072 |
Modular degree for the optimal curve |
Δ |
-35979264 = -1 · 216 · 32 · 61 |
Discriminant |
Eigenvalues |
2- 3+ -1 -3 -3 5 -6 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1,289] |
[a1,a2,a3,a4,a6] |
Generators |
[-5:12:1] [-3:16:1] |
Generators of the group modulo torsion |
j |
-4/549 |
j-invariant |
L |
4.9971217999107 |
L(r)(E,1)/r! |
Ω |
1.6414789515954 |
Real period |
R |
0.38053501958205 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999996 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
11712h1 2928d1 35136bu1 |
Quadratic twists by: -4 8 -3 |