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

• Label: 2.23.o_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

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:	$\pm0.760387042310$, $\pm0.760387042310$
Angle rank:	$1$ (numerical)
Jacobians:	$2$
Cyclic group of points:	no
Non-cyclic primes:	$31$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$961$	$277729$	$144672784$	$78899753881$	$41373466992841$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$38$	$524$	$11888$	$281940$	$6428098$	$148045358$	$3404948830$	$78309903844$	$1801157393744$	$41426502960764$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 2 curves (of which all are hyperelliptic):

• $y^2=17 x^6+x^5+2 x^4+2 x^2+x+17$
• $y^2=16 x^6+10 x^5+6 x^4+9 x^2+2 x+6$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{23}$

The isogeny class factors as 1.23.h^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.

Twist	Extension degree	Common base change
2.23.ao_dr	$2$	(not in LMFDB)
2.23.a_ad	$2$	(not in LMFDB)
2.23.ah_ba	$3$	(not in LMFDB)