Atkin-Lehner |
2- 3+ 61- |
Signs for the Atkin-Lehner involutions |
Class |
11712bc |
Isogeny class |
Conductor |
11712 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
3840 |
Modular degree for the optimal curve |
Δ |
-23986176 = -1 · 217 · 3 · 61 |
Discriminant |
Eigenvalues |
2- 3+ -3 -2 -6 -4 5 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,63,-159] |
[a1,a2,a3,a4,a6] |
Generators |
[5:16:1] |
Generators of the group modulo torsion |
j |
207646/183 |
j-invariant |
L |
2.1178642867349 |
L(r)(E,1)/r! |
Ω |
1.1719229156734 |
Real period |
R |
0.4517925749233 |
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 |
11712p1 2928c1 35136cq1 |
Quadratic twists by: -4 8 -3 |