Properties

Label 2.19.aq_dy
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:  $( 1 - 8 x + 19 x^{2} )^{2}$
Frobenius angles:  $\pm0.130073469147$, $\pm0.130073469147$
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
$A(\F_{q^r})$ 144 112896 46294416 16995815424 6138164811024 2214310804183296 799109393158339344 288450195053661978624 104127980635077893874576 37590009037051531288709376

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 310 6748 130414 2478964 47067046 893986636 16984080094 322689651172 6131072060950

Decomposition

1.19.ai 2

Base change

This is a primitive isogeny class.