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

• Label: 2.43.a_df
• 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:	$1 + 83 x^{2} + 1849 x^{4}$
Frobenius angles:	$\pm0.457838391839$, $\pm0.542161608161$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\zeta_{12})\)
Galois group:	$C_2^2$
Jacobians:	$26$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$1933$	$3736489$	$6321474436$	$11666398503321$	$21611482384956493$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$44$	$2016$	$79508$	$3412420$	$147008444$	$6321585822$	$271818611108$	$11688193587844$	$502592611936844$	$21611482456628736$

Jacobians and polarizations

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

• $y^2=37 x^6+37 x^5+9 x^4+31 x^3+11 x^2+15$
• $y^2=25 x^6+25 x^5+27 x^4+7 x^3+33 x^2+2$
• $y^2=33 x^6+20 x^5+17 x^4+28 x^3+26 x^2+14 x+20$
• $y^2=13 x^6+17 x^5+8 x^4+41 x^3+35 x^2+42 x+17$
• $y^2=11 x^6+40 x^5+7 x^4+10 x^3+11 x^2+22 x+41$
• $y^2=33 x^6+34 x^5+21 x^4+30 x^3+33 x^2+23 x+37$
• $y^2=17 x^6+29 x^5+6 x^4+32 x^3+21 x^2+20 x+18$
• $y^2=8 x^6+x^5+18 x^4+10 x^3+20 x^2+17 x+11$
• $y^2=38 x^6+6 x^5+40 x^4+42 x^3+40 x^2+30 x+8$
• $y^2=28 x^6+18 x^5+34 x^4+40 x^3+34 x^2+4 x+24$
• $y^2=13 x^6+40 x^5+2 x^4+13 x^3+29 x^2+36 x+5$
• $y^2=x^6+2 x^5+8 x^4+32 x^3+27 x^2+6 x+21$
• $y^2=3 x^6+6 x^5+24 x^4+10 x^3+38 x^2+18 x+20$
• $y^2=10 x^6+14 x^5+3 x^4+29 x^3+28 x^2+5 x+32$
• $y^2=30 x^6+42 x^5+9 x^4+x^3+41 x^2+15 x+10$
• $y^2=36 x^6+30 x^5+x^4+28 x^3+19 x^2+35 x+41$
• $y^2=22 x^6+4 x^5+3 x^4+41 x^3+14 x^2+19 x+37$
• $y^2=19 x^6+40 x^5+8 x^4+10 x^3+14 x^2+21 x+26$
• $y^2=14 x^6+34 x^5+24 x^4+30 x^3+42 x^2+20 x+35$
• $y^2=23 x^6+28 x^5+3 x^4+29 x^3+35 x^2+39 x+17$
• $y^2=26 x^6+41 x^5+9 x^4+x^3+19 x^2+31 x+8$
• $y^2=30 x^6+7 x^5+13 x^4+16 x^3+31 x^2+30 x+11$
• $y^2=4 x^6+21 x^5+39 x^4+5 x^3+7 x^2+4 x+33$
• $y^2=39 x^6+37 x^5+5 x^4+12 x^3+34 x^2+33 x+17$
• $y^2=31 x^6+25 x^5+15 x^4+36 x^3+16 x^2+13 x+8$
• $y^2=10 x^6+x^5+26 x^4+41 x^3+40 x^2+10 x+5$

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 \(\Q(\zeta_{12})\).

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

The base change of $A$ to $\F_{43^{2}}$ is 1.1849.df^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-3}) \)$)$

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.a_acj	$3$	(not in LMFDB)
2.43.a_aw	$3$	(not in LMFDB)
2.43.aba_jv	$4$	(not in LMFDB)