Abelian variety isogeny class 3.23.ax_jl_acfy over $\F_{23}$

• Label: 3.23.ax_jl_acfy
• Base field: $\F_{23}$
• Dimension: $3$
• $p$-rank: $3$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: no

Invariants

Base field:	$\F_{23}$
Dimension:	$3$
L-polynomial:	$( 1 - 7 x + 23 x^{2} )( 1 - 8 x + 23 x^{2} )^{2}$
	$1 - 23 x + 245 x^{2} - 1506 x^{3} + 5635 x^{4} - 12167 x^{5} + 12167 x^{6}$
Frobenius angles:	$\pm0.186011988595$, $\pm0.186011988595$, $\pm0.239612957690$
Angle rank:	$2$ (numerical)

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

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$4352$	$138149888$	$1834326029312$	$22112551793852416$	$267216870355299580672$

Point counts of the (virtual) curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$1$	$491$	$12388$	$282359$	$6450371$	$148086092$	$3404899709$	$78310486415$	$1801147503244$	$41426483787971$

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 $\F_{23}$.

Endomorphism algebra over $\F_{23}$

The isogeny class factors as 1.23.ai^2 $\times$ 1.23.ah and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.23.ai^2 : $\mathrm{M}_{2}($\(\Q(\sqrt{-7}) \)$)$
• 1.23.ah : \(\Q(\sqrt{-43}) \).

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

Twist	Extension degree	Common base change
3.23.aj_v_bi	$2$	(not in LMFDB)
3.23.ah_f_ew	$2$	(not in LMFDB)
3.23.h_f_aew	$2$	(not in LMFDB)
3.23.j_v_abi	$2$	(not in LMFDB)
3.23.x_jl_cfy	$2$	(not in LMFDB)
3.23.b_i_dd	$3$	(not in LMFDB)