Properties

Label 2.23.an_db
Base Field $\F_{23}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{23}$
Dimension:  $2$
Weil polynomial:  $1 - 13 x + 79 x^{2} - 299 x^{3} + 529 x^{4}$
Frobenius angles:  $\pm0.0326071920932$, $\pm0.382576753817$
Angle rank:  $2$ (numerical)
Number field:  4.0.105413.1
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
$A(\F_{q^r})$ 297 273537 147860559 78011931789 41366636202672 21909523257122193 11592747667651662963 6132623535615212438517 3244148846780369722481133 1716155098876077779099043072

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 11 519 12155 278771 6427036 148001427 3404799409 78311152819 1801151516021 41426493532734

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.