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

• Label: 2.43.a_acw
• Base field: $\F_{43}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: yes
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{43}$
Dimension:	$2$
L-polynomial:	$1 - 74 x^{2} + 1849 x^{4}$
Frobenius angles:	$\pm0.0850865380712$, $\pm0.914913461929$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-3}, \sqrt{10})\)
Galois group:	$C_2^2$
Jacobians:	$26$
Isomorphism classes:	152

This isogeny class is simple but not 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$1776$	$3154176$	$6321368304$	$11676053016576$	$21611482575617136$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$44$	$1702$	$79508$	$3415246$	$147008444$	$6321373558$	$271818611108$	$11688207630238$	$502592611936844$	$21611482837950022$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 26 curves (of which all are hyperelliptic):

• $y^2=18 x^6+20 x^5+34 x^4+41 x^3+14 x^2+25 x+16$
• $y^2=x^6+7 x^3+42$
• $y^2=17 x^6+3 x^5+39 x^4+10 x^3+41 x^2+33 x+29$
• $y^2=19 x^6+29 x^5+x^4+23 x^3+35 x^2+31 x+26$
• $y^2=33 x^6+5 x^4+9 x^3+5 x^2+12 x+25$
• $y^2=34 x^6+19 x^5+23 x^4+24 x^3+20 x^2+19 x+9$
• $y^2=34 x^6+17 x^5+20 x^4+20 x^3+19 x^2+29 x+12$
• $y^2=16 x^6+8 x^5+17 x^4+17 x^3+14 x^2+x+36$
• $y^2=38 x^5+34 x^4+20 x^3+22 x^2+23 x+22$
• $y^2=x^6+3 x^3+27$
• $y^2=25 x^6+15 x^5+40 x^4+19 x^3+26 x^2+23 x+7$
• $y^2=x^6+20 x^3+2$
• $y^2=14 x^5+20 x^4+25 x^3+38 x^2+18 x+28$
• $y^2=x^6+x^3+42$
• $y^2=41 x^6+21 x^5+40 x^4+16 x^3+37 x^2+34 x+20$
• $y^2=x^6+12 x^3+8$
• $y^2=9 x^6+x^5+41 x^4+30 x^3+28 x^2+32 x+31$
• $y^2=37 x^6+7 x^5+31 x^4+3 x^3+6 x^2+10 x+32$
• $y^2=x^6+33 x^3+32$
• $y^2=18 x^6+38 x^5+40 x^4+35 x^3+7 x^2+35 x+27$
• $y^2=14 x^6+33 x^5+20 x^4+19 x^3+17 x^2+26 x+19$
• $y^2=21 x^6+9 x^4+22 x^3+27 x^2+28 x+23$
• $y^2=5 x^6+7 x^5+6 x^4+2 x^3+18 x^2+20 x+6$
• $y^2=28 x^6+5 x^5+42 x^4+23 x^3+26 x^2+38 x+16$
• $y^2=40 x^6+30 x^5+40 x^4+18 x^3+28 x^2+19 x+12$
• $y^2=19 x^6+31 x^5+12 x^4+22 x^3+23 x^2+24 x+6$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{43^{2}}$.

Endomorphism algebra over $\F_{43}$

The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-3}, \sqrt{10})\).

Endomorphism algebra over $\overline{\F}_{43}$

The base change of $A$ to $\F_{43^{2}}$ is 1.1849.acw^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-30}) \)$)$

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
2.43.ag_cd	$3$	(not in LMFDB)
2.43.g_cd	$3$	(not in LMFDB)
2.43.a_cw	$4$	(not in LMFDB)