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

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

Invariants

Base field:	$\F_{23}$
Dimension:	$2$
L-polynomial:	$1 + 12 x + 74 x^{2} + 276 x^{3} + 529 x^{4}$
Frobenius angles:	$\pm0.607271105589$, $\pm0.872158939421$
Angle rank:	$2$ (numerical)
Number field:	4.0.18432.2
Galois group:	$C_4$
Jacobians:	$14$

This isogeny class is simple and 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$892$	$281872$	$146731324$	$78256687104$	$41445127160572$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$36$	$534$	$12060$	$279646$	$6439236$	$148043382$	$3404632764$	$78312048574$	$1801150562916$	$41426506930134$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 14 curves (of which all are hyperelliptic):

• $y^2=7 x^6+20 x^4+9 x^3+3 x^2+21 x+9$
• $y^2=2 x^6+6 x^4+14 x^3+13 x^2+10 x+19$
• $y^2=22 x^6+4 x^5+18 x^3+7 x^2+x+6$
• $y^2=12 x^6+10 x^5+22 x^4+21 x^3+17 x^2+21 x+7$
• $y^2=3 x^6+22 x^5+21 x^3+22 x^2+11 x+2$
• $y^2=9 x^6+8 x^5+13 x^4+4 x^3+16 x^2+17 x+9$
• $y^2=12 x^6+16 x^5+7 x^4+12 x^3+9 x^2+18 x+1$
• $y^2=12 x^6+11 x^5+20 x^4+18 x^3+19 x^2+2$
• $y^2=12 x^6+x^5+20 x^4+20 x^3+2 x^2+18 x+19$
• $y^2=16 x^6+6 x^5+8 x^4+20 x^3+10 x^2+7 x+15$
• $y^2=5 x^6+15 x^5+4 x^4+11 x^3+x^2+14 x+9$
• $y^2=4 x^6+12 x^5+14 x^4+18 x^3+19 x^2+15 x+16$
• $y^2=11 x^6+19 x^5+12 x^4+10 x^3+13 x^2+9 x+4$
• $y^2=4 x^6+2 x^5+12 x^4+2 x^3+13 x^2+11 x+22$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{23}$

The endomorphism algebra of this simple isogeny class is 4.0.18432.2.

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.am_cw	$2$	(not in LMFDB)