Abelian variety isogeny class 2.43.ax_ij over $\F_{43}$

• Label: 2.43.ax_ij
• Base field: $\F_{43}$
• 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:	$\F_{43}$
Dimension:	$2$
L-polynomial:	$1 - 23 x + 217 x^{2} - 989 x^{3} + 1849 x^{4}$
Frobenius angles:	$\pm0.0878968508670$, $\pm0.209239299354$
Angle rank:	$2$ (numerical)
Number field:	4.0.20525.1
Galois group:	$D_{4}$
Jacobians:	$3$
Isomorphism classes:	3

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$1055$	$3248345$	$6308637305$	$11693538506525$	$21614336225262000$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$21$	$1755$	$79347$	$3420363$	$147027856$	$6321487215$	$271819096017$	$11688200798883$	$502592605607451$	$21611482304584150$

Jacobians and polarizations

This isogeny class contains the Jacobians of 3 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=28x^6+21x^5+31x^4+19x^3+32x^2+16x+15$
• $y^2=27x^6+42x^5+17x^4+22x^3+36x^2+15x+41$
• $y^2=29x^6+7x^5+21x^4+16x^3+17x^2+14x+18$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{43}$.

Endomorphism algebra over $\F_{43}$

The endomorphism algebra of this simple isogeny class is 4.0.20525.1.

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
2.43.x_ij	$2$	(not in LMFDB)