Abelian variety isogeny class 2.23.a_abs over $\F_{23}$

• Label: 2.23.a_abs
• 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: no

Invariants

Base field:	$\F_{23}$
Dimension:	$2$
L-polynomial:	$1 - 44 x^{2} + 529 x^{4}$
Frobenius angles:	$\pm0.0471039619283$, $\pm0.952896038072$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-2}, \sqrt{-5})\)
Galois group:	$C_2^2$
Jacobians:	$0$

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

Newton polygon

This isogeny class is ordinary.

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

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$486$	$236196$	$148020534$	$77820913296$	$41426510044086$

Point counts of the (virtual) curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$24$	$442$	$12168$	$278086$	$6436344$	$148005178$	$3404825448$	$78310562878$	$1801152661464$	$41426508874522$

Jacobians and polarizations

This isogeny class is principally polarizable, but does not contain a Jacobian.

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{23^{2}}$.

Endomorphism algebra over $\F_{23}$

The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-2}, \sqrt{-5})\).

Endomorphism algebra over $\overline{\F}_{23}$

The base change of $A$ to $\F_{23^{2}}$ is 1.529.abs^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-5}) \)$)$

Base change

This is a primitive isogeny class.

Twists

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

Twist	Extension degree	Common base change
2.23.a_bs	$4$	(not in LMFDB)
2.23.ac_c	$8$	(not in LMFDB)
2.23.c_c	$8$	(not in LMFDB)