Properties

Label 2.19.an_cy
Base Field $\F_{19}$
Dimension $2$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{19}$
Dimension:  $2$
L-polynomial:  $1 - 13 x + 76 x^{2} - 247 x^{3} + 361 x^{4}$
Frobenius angles:  $\pm0.0603553363735$, $\pm0.329969159439$
Angle rank:  $2$ (numerical)
Number field:  4.0.43928.1
Galois group:  $D_{4}$
Jacobians:  2

This isogeny class is simple and geometrically simple.

Newton polygon

$p$-rank:  $1$
Slopes:  $[0, 1/2, 1/2, 1]$

Point counts

This isogeny class contains the Jacobians of 2 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 178 124244 47214856 16965766688 6122994315838 2212400143668416 798963727685986222 288443056776740398208 104127764851098169084072 37590001032051721372609044

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 7 345 6886 130185 2472837 47026434 893823679 16983659793 322688982466 6131070755305

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{19}$
The endomorphism algebra of this simple isogeny class is 4.0.43928.1.
All geometric endomorphisms are defined over $\F_{19}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.19.n_cy$2$(not in LMFDB)