Properties

Label 2.19.ap_dq
Base Field $\F_{19}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Does not contain a Jacobian

Learn more about

Invariants

Base field:  $\F_{19}$
Dimension:  $2$
Weil polynomial:  $( 1 - 8 x + 19 x^{2} )( 1 - 7 x + 19 x^{2} )$
Frobenius angles:  $\pm0.130073469147$, $\pm0.203259864187$
Angle rank:  $1$ (numerical)

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 156 117936 47056464 17068169664 6142403868276 2214310804183296 799070872855699236 288444096418094233344 104127350297602681851984 37589961044115088796272176

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 325 6860 130969 2480675 47067046 893943545 16983721009 322687697780 6131064233125

Decomposition

1.19.ai $\times$ 1.19.ah

Base change

This is a primitive isogeny class.