Properties

Label 2.23.an_dg
Base field $\F_{23}$
Dimension $2$
$p$-rank $2$
Ordinary yes
Supersingular no
Simple yes
Geometrically simple yes
Primitive yes
Principally polarizable yes
Contains a Jacobian yes

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Invariants

Base field:  $\F_{23}$
Dimension:  $2$
L-polynomial:  $1 - 13 x + 84 x^{2} - 299 x^{3} + 529 x^{4}$
Frobenius angles:  $\pm0.148876346239$, $\pm0.346866314170$
Angle rank:  $2$ (numerical)
Number field:  4.0.390728.1
Galois group:  $D_{4}$
Jacobians:  $4$
Isomorphism classes:  4

This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

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

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $302$ $279652$ $150266744$ $78501672224$ $41427265132522$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $11$ $529$ $12350$ $280521$ $6436461$ $148035322$ $3404914979$ $78311872689$ $1801156445426$ $41426512933209$

Jacobians and polarizations

This isogeny class contains the Jacobians of 4 curves (of which all are hyperelliptic), and hence is principally polarizable:

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{23}$.

Endomorphism algebra over $\F_{23}$
The endomorphism algebra of this simple isogeny class is 4.0.390728.1.

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_dg$2$(not in LMFDB)