Properties

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

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Invariants

Base field:  $\F_{19}$
Dimension:  $2$
Weil polynomial:  $( 1 - 7 x + 19 x^{2} )( 1 - 5 x + 19 x^{2} )$
Frobenius angles:  $\pm0.203259864187$, $\pm0.305569972467$
Angle rank:  $2$ (numerical)

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 195 131625 48550320 17134547625 6138171800475 2213253727776000 798971085669032835 288438938659422383625 104127294467636946782640 37589973152955087548165625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 8 364 7076 131476 2478968 47044582 893831912 16983417316 322687524764 6131066208124

Decomposition

1.19.ah $\times$ 1.19.af

Base change

This is a primitive isogeny class.