Properties

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

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Invariants

Base field:  $\F_{23}$
Dimension:  $2$
L-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:  $D_{4}$
Jacobians:  2

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class contains the Jacobians of 2 curves, 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 and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The endomorphism algebra of this simple isogeny class is 4.0.105413.1.
All geometric endomorphisms are defined over $\F_{23}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.23.n_db$2$(not in LMFDB)