Properties

Label 2.19.aj_bq
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:  $1 - 9 x + 42 x^{2} - 171 x^{3} + 361 x^{4}$
Frobenius angles:  $\pm0.0659896528252$, $\pm0.482872009315$
Angle rank:  $2$ (numerical)
Number field:  4.0.257725.1
Galois group:  $D_4$

This isogeny class is simple.

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
$A(\F_{q^r})$ 224 130816 46315136 16828693504 6125033342624 2213719738617856 799019969453885984 288437778553232093184 104127286208732858562176 37590014147756807110264576

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 11 365 6752 129129 2473661 47054486 893886599 16983349009 322687499168 6131072894525

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.