Properties

Label 2.19.ak_cl
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:  $( 1 - 5 x + 19 x^{2} )^{2}$
Frobenius angles:  $\pm0.305569972467$, $\pm0.305569972467$
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
$A(\F_{q^r})$ 225 140625 49280400 17128265625 6129709430625 2212197156000000 798909821626178025 288439879410444515625 104127868974500422131600 37590033254766349306640625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 10 388 7180 131428 2475550 47022118 893763370 16983472708 322689305140 6131076010948

Decomposition

1.19.af 2

Base change

This is a primitive isogeny class.