Atkin-Lehner |
2- 3- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
11712be |
Isogeny class |
Conductor |
11712 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
11520 |
Modular degree for the optimal curve |
Δ |
-124344336384 = -1 · 223 · 35 · 61 |
Discriminant |
Eigenvalues |
2- 3- -1 2 2 -4 -7 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-321,-17217] |
[a1,a2,a3,a4,a6] |
Generators |
[111:1152:1] |
Generators of the group modulo torsion |
j |
-13997521/474336 |
j-invariant |
L |
5.4100542934705 |
L(r)(E,1)/r! |
Ω |
0.45517846031181 |
Real period |
R |
0.59427837268096 |
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 |
11712b1 2928j1 35136bq1 |
Quadratic twists by: -4 8 -3 |