Atkin-Lehner |
2+ 3- 7- |
Signs for the Atkin-Lehner involutions |
Class |
14112p |
Isogeny class |
Conductor |
14112 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
-806887666368 = -1 · 26 · 37 · 78 |
Discriminant |
Eigenvalues |
2+ 3- 0 7- -2 2 4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,735,-42532] |
[a1,a2,a3,a4,a6] |
Generators |
[77:686:1] |
Generators of the group modulo torsion |
j |
8000/147 |
j-invariant |
L |
4.7078732836074 |
L(r)(E,1)/r! |
Ω |
0.4352928646152 |
Real period |
R |
1.3519269629451 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
14112bu1 28224bk2 4704s1 2016f1 |
Quadratic twists by: -4 8 -3 -7 |