Properties

Label 2.19.al_ci
Base Field $\F_{19}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

Learn more about

Invariants

Base field:  $\F_{19}$
Dimension:  $2$
L-polynomial:  $1 - 11 x + 60 x^{2} - 209 x^{3} + 361 x^{4}$
Frobenius angles:  $\pm0.0899168499442$, $\pm0.402539378619$
Angle rank:  $2$ (numerical)
Number field:  4.0.444312.2
Galois group:  $D_{4}$
Jacobians:  4

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class contains the Jacobians of 4 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 202 129684 47196088 16911831072 6122057290822 2213225055301824 799072753925610646 288447636123620162688 104127515019253716936856 37589972043459737592720084

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 9 361 6882 129769 2472459 47043970 893945649 16983929425 322688208246 6131066027161

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{19}$
The endomorphism algebra of this simple isogeny class is 4.0.444312.2.
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.l_ci$2$(not in LMFDB)