Properties

Label 2.23.ao_dp
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:  $1 - 14 x + 93 x^{2} - 322 x^{3} + 529 x^{4}$
Frobenius angles:  $\pm0.159380640241$, $\pm0.302130010970$
Angle rank:  $2$ (numerical)
Number field:  4.0.82496.2
Galois group:  $D_{4}$
Jacobians:  5

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 5 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 287 275233 150441956 78670674089 41451663754207 21915195658627600 11592835985766017423 6132627581709802642889 3244154970756963721473764 1716156208520934448363985953

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 10 520 12364 281124 6440250 148039750 3404825350 78311204484 1801154916052 41426520318600

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The endomorphism algebra of this simple isogeny class is 4.0.82496.2.
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.o_dp$2$(not in LMFDB)