Properties

Label 2.19.aj_bu
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:  $( 1 - 8 x + 19 x^{2} )( 1 - x + 19 x^{2} )$
Frobenius angles:  $\pm0.130073469147$, $\pm0.46340680248$
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
$A(\F_{q^r})$ 228 134064 47056464 16905470400 6130377927948 2214310804183296 799096559016987228 288443121410865657600 104127350297602681851984 37590003660735378639373104

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 11 373 6860 129721 2475821 47067046 893972279 16983663601 322687697780 6131071184053

Decomposition

1.19.ai $\times$ 1.19.ab

Base change

This is a primitive isogeny class.