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

• Label: 2.43.a_l
• 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:	$1 + 11 x^{2} + 1849 x^{4}$
Frobenius angles:	$\pm0.270412947769$, $\pm0.729587052231$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{3}, \sqrt{-97})\)
Galois group:	$C_2^2$
Jacobians:	$30$
Isomorphism classes:	72
Cyclic group of points:	yes

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$1861$	$3463321$	$6321303364$	$11712678019641$	$21611482489174261$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$44$	$1872$	$79508$	$3425956$	$147008444$	$6321243678$	$271818611108$	$11688188362948$	$502592611936844$	$21611482665064272$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 30 curves (of which all are hyperelliptic):

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

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 \(\Q(\sqrt{3}, \sqrt{-97})\).

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

The base change of $A$ to $\F_{43^{2}}$ is 1.1849.l^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-291}) \)$)$

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.a_al	$4$	(not in LMFDB)
2.43.ap_eo	$12$	(not in LMFDB)
2.43.p_eo	$12$	(not in LMFDB)