Properties

Label 2.19.ak_cc
Base Field $\F_{19}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

Learn more about

Invariants

Base field:  $\F_{19}$
Dimension:  $2$
Weil polynomial:  $( 1 - 8 x + 19 x^{2} )( 1 - 2 x + 19 x^{2} )$
Frobenius angles:  $\pm0.130073469147$, $\pm0.426318466621$
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
$A(\F_{q^r})$ 216 133056 47396664 16933238784 6127476737976 2213929646824896 799111425953312856 288447031986733154304 104127345957440010149784 37589970685374618644016576

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 10 370 6910 129934 2474650 47058946 893988910 16983893854 322687684330 6131065805650

Decomposition

1.19.ai $\times$ 1.19.ac

Base change

This is a primitive isogeny class.