Properties

Label 2.19.al_co
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:  $( 1 - 7 x + 19 x^{2} )( 1 - 4 x + 19 x^{2} )$
Frobenius angles:  $\pm0.203259864187$, $\pm0.348268167089$
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
$A(\F_{q^r})$ 208 134784 48577984 17093306880 6133488510448 2213192742598656 799009155384017968 288443170343851960320 104127369536184992880064 37589944905494015471858304

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 9 373 7080 131161 2477079 47043286 893874501 16983666481 322687757400 6131061600853

Decomposition

1.19.ah $\times$ 1.19.ae

Base change

This is a primitive isogeny class.