Properties

Label 2.23.am_ct
Base field $\F_{23}$
Dimension $2$
$p$-rank $2$
Ordinary yes
Supersingular no
Simple yes
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:  $1 - 12 x + 71 x^{2} - 276 x^{3} + 529 x^{4}$
Frobenius angles:  $\pm0.0764113711973$, $\pm0.409744704531$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-3}, \sqrt{11})\)
Galois group:  $C_2^2$
Jacobians:  $6$
Isomorphism classes:  6

This isogeny class is simple but not 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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $313$ $278257$ $148032724$ $78016862889$ $41382431470873$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $12$ $528$ $12168$ $278788$ $6429492$ $148029558$ $3404945052$ $78311536516$ $1801152661464$ $41426508436368$

Jacobians and polarizations

This isogeny class contains the Jacobians of 6 curves (of which all are hyperelliptic), and hence is principally polarizable:

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{23^{6}}$.

Endomorphism algebra over $\F_{23}$
The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-3}, \sqrt{11})\).
Endomorphism algebra over $\overline{\F}_{23}$
The base change of $A$ to $\F_{23^{6}}$ is 1.148035889.aeru 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-33}) \)$)$
Remainder of endomorphism lattice by field

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.m_ct$2$(not in LMFDB)
2.23.a_c$3$(not in LMFDB)
2.23.m_ct$3$(not in LMFDB)

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

TwistExtension degreeCommon base change
2.23.m_ct$2$(not in LMFDB)
2.23.a_c$3$(not in LMFDB)
2.23.m_ct$3$(not in LMFDB)
2.23.a_ac$12$(not in LMFDB)