Properties

Label 3.23.a_f_ey
Base field $\F_{23}$
Dimension $3$
$p$-rank $3$
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:  $3$
L-polynomial:  $1 + 5 x^{2} + 128 x^{3} + 115 x^{4} + 12167 x^{6}$
Frobenius angles:  $\pm0.253816572843$, $\pm0.427808404135$, $\pm0.874630901049$
Angle rank:  $3$ (numerical)
Number field:  6.0.19078384.1
Galois group:  $S_4\times C_2$

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:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $12416$ $150978560$ $1859032420736$ $21946774926131200$ $266502710880498943616$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $24$ $540$ $12552$ $280252$ $6433144$ $148056540$ $3404744808$ $78311122812$ $1801146117336$ $41426513484700$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 1298 hyperelliptic curves, but it is unknown how many Jacobians of non-hyperelliptic curves it contains:

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 6.0.19078384.1.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.

TwistExtension degreeCommon base change
3.23.a_f_aey$2$(not in LMFDB)