Properties

Label 2.19.an_da
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:  $( 1 - 8 x + 19 x^{2} )( 1 - 5 x + 19 x^{2} )$
Frobenius angles:  $\pm0.130073469147$, $\pm0.305569972467$
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
$A(\F_{q^r})$ 180 126000 47764080 17061912000 6133935663900 2213253727776000 799009601161295340 288445037185938528000 104127924804774190734960 37590021145906989987150000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 7 349 6964 130921 2477257 47044582 893875003 16983776401 322689478156 6131074035949

Decomposition

1.19.ai $\times$ 1.19.af

Base change

This is a primitive isogeny class.