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

• Label: 2.43.j_bm
• 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:	$1 + 9 x + 38 x^{2} + 387 x^{3} + 1849 x^{4}$
Frobenius angles:	$\pm0.407408251406$, $\pm0.925925081928$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-3}, \sqrt{-91})\)
Galois group:	$C_2^2$
Jacobians:	$38$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$2284$	$3407728$	$6390403600$	$11675653089984$	$21609353546697604$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$53$	$1845$	$80372$	$3415129$	$146993963$	$6321307830$	$271819482281$	$11688206930929$	$502592567097836$	$21611482228966725$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 38 curves (of which all are hyperelliptic):

• $y^2=13 x^6+15 x^5+42 x^3+12 x^2+19 x+33$
• $y^2=38 x^6+26 x^5+28 x^4+34 x^3+35 x^2+6 x+14$
• $y^2=35 x^6+25 x^5+x^4+26 x^2+27 x+31$
• $y^2=15 x^6+41 x^5+19 x^4+34 x^3+40 x^2+34 x+23$
• $y^2=14 x^6+19 x^5+21 x^4+37 x^3+7 x^2+5 x+36$
• $y^2=18 x^6+40 x^5+17 x^4+28 x^3+12 x^2+22 x+1$
• $y^2=11 x^6+39 x^5+20 x^4+9 x^3+29 x+18$
• $y^2=38 x^6+38 x^5+34 x^4+4 x^3+23 x^2+21 x+21$
• $y^2=39 x^6+7 x^5+2 x^4+38 x^3+27 x^2+19 x+29$
• $y^2=33 x^6+8 x^5+39 x^4+26 x^3+27 x^2+9 x+24$
• $y^2=16 x^6+11 x^5+33 x^4+34 x^3+15 x^2+38 x+6$
• $y^2=2 x^6+29 x^5+27 x^4+19 x^3+34 x^2+10 x+9$
• $y^2=13 x^6+40 x^5+21 x^4+28 x^3+7 x^2+x+33$
• $y^2=11 x^6+18 x^5+38 x^4+18 x^3+28 x^2+16 x+31$
• $y^2=30 x^6+11 x^5+x^4+16 x^3+8 x^2+3 x+14$
• $y^2=22 x^6+4 x^5+23 x^4+34 x^3+14 x^2+3 x+22$
• $y^2=x^6+35 x^5+37 x^4+11 x^3+32 x^2+4 x+7$
• $y^2=36 x^6+16 x^5+29 x^4+23 x^3+14 x^2+35 x+15$
• $y^2=36 x^6+3 x^5+24 x^4+8 x^2+18 x+16$
• $y^2=31 x^6+20 x^5+31 x^4+23 x^3+37 x^2+42 x+1$
• and

• $y^2=37 x^6+42 x^5+18 x^4+3 x^3+11 x^2+10 x+29$
• $y^2=24 x^6+29 x^5+42 x^4+10 x^3+7 x^2+15 x+30$
• $y^2=36 x^6+31 x^5+23 x^4+34 x^3+10 x^2+15 x+33$
• $y^2=42 x^6+3 x^5+4 x^4+40 x^3+19 x^2+25 x+1$
• $y^2=38 x^6+40 x^5+31 x^4+x^3+11 x^2+40 x+24$
• $y^2=36 x^6+11 x^5+35 x^4+9 x^3+21 x^2+7 x+37$
• $y^2=38 x^6+41 x^5+15 x^4+42 x^3+36 x^2+27 x+11$
• $y^2=4 x^6+38 x^5+27 x^4+24 x^3+6 x^2+9 x+41$
• $y^2=40 x^6+8 x^5+34 x^4+37 x^3+42 x^2+2 x+42$
• $y^2=26 x^6+40 x^5+16 x^4+39 x^3+32 x^2+24 x+17$
• $y^2=14 x^6+x^5+4 x^4+12 x^3+17 x^2+15 x+18$
• $y^2=34 x^6+7 x^5+23 x^4+27 x^3+38 x^2+11 x+34$
• $y^2=15 x^6+38 x^5+15 x^4+6 x^3+14 x^2+16 x+21$
• $y^2=24 x^6+34 x^5+12 x^4+10 x^3+27 x^2+4 x+34$
• $y^2=31 x^6+24 x^5+39 x^4+42 x^3+13 x^2+12 x+8$
• $y^2=23 x^6+35 x^5+32 x^4+31 x^3+6 x^2+25 x+13$
• $y^2=7 x^6+10 x^5+27 x^4+36 x^3+10 x^2+26 x+2$
• $y^2=26 x^6+42 x^5+29 x^4+32 x^3+35 x^2+7 x+18$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{43^{3}}$.

Endomorphism algebra over $\F_{43}$

The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-3}, \sqrt{-91})\).

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

The base change of $A$ to $\F_{43^{3}}$ is 1.79507.qq^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-91}) \)$)$

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.aj_bm	$2$	(not in LMFDB)
2.43.as_gl	$3$	(not in LMFDB)
2.43.aj_bm	$6$	(not in LMFDB)