Properties

Label 2.23.an_dc
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:  $1 - 13 x + 80 x^{2} - 299 x^{3} + 529 x^{4}$
Frobenius angles:  $\pm0.0682102518540$, $\pm0.376537722378$
Angle rank:  $2$ (numerical)
Number field:  4.0.357192.2
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
$A(\F_{q^r})$ 298 274756 148340824 78112031776 41380432054798 21911139485384512 11592972615898174414 6132660480956699607168 3244154257259082245098168 1716155725194537021383783716

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 11 521 12194 279129 6429181 148012346 3404865475 78311624593 1801154519918 41426508651521

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The endomorphism algebra of this simple isogeny class is 4.0.357192.2.
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_dc$2$(not in LMFDB)