Properties

Label 2.19.am_cw
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:  $( 1 - 6 x + 19 x^{2} )^{2}$
Frobenius angles:  $\pm0.258380448083$, $\pm0.258380448083$
Angle rank:  $1$ (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
$A(\F_{q^r})$ 196 132496 48804196 17171481600 6140553384196 2213111967788176 798918529220525476 288432756057522585600 104126968026280916546116 37589989261020791711932816

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 8 366 7112 131758 2479928 47041566 893773112 16983053278 322686513128 6131068835406

Decomposition

1.19.ag 2

Base change

This is a primitive isogeny class.