Properties

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

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Invariants

Base field:  $\F_{23}$
Dimension:  $2$
L-polynomial:  $( 1 - 7 x + 23 x^{2} )^{2}$
  $1 - 14 x + 95 x^{2} - 322 x^{3} + 529 x^{4}$
Frobenius angles:  $\pm0.239612957690$, $\pm0.239612957690$
Angle rank:  $1$ (numerical)
Jacobians:  $2$

This isogeny class is not 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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $289$ $277729$ $151486864$ $78899753881$ $41479615178089$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $10$ $524$ $12448$ $281940$ $6444590$ $148045358$ $3404702066$ $78309903844$ $1801147929184$ $41426502960764$

Jacobians and polarizations

This isogeny class contains the Jacobians of 2 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 isogeny class factors as 1.23.ah 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-43}) \)$)$

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

TwistExtension degreeCommon base change
2.23.a_ad$2$(not in LMFDB)
2.23.o_dr$2$(not in LMFDB)
2.23.h_ba$3$(not in LMFDB)

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

TwistExtension degreeCommon base change
2.23.a_ad$2$(not in LMFDB)
2.23.o_dr$2$(not in LMFDB)
2.23.h_ba$3$(not in LMFDB)
2.23.a_d$4$(not in LMFDB)
2.23.ah_ba$6$(not in LMFDB)