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

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

Invariants

Base field:	$\F_{43}$
Dimension:	$2$
L-polynomial:	$( 1 + 5 x + 43 x^{2} )^{2}$
	$1 + 10 x + 111 x^{2} + 430 x^{3} + 1849 x^{4}$
Frobenius angles:	$\pm0.624505058506$, $\pm0.624505058506$
Angle rank:	$1$ (numerical)
Jacobians:	$12$
Cyclic group of points:	no
Non-cyclic primes:	$7$

This isogeny class is not 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$2401$	$3651921$	$6239104144$	$11688049850841$	$21618091141984561$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$54$	$1972$	$78468$	$3418756$	$147053394$	$6321140278$	$271817792118$	$11688213951748$	$502592578782684$	$21611481891066772$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 12 curves (of which all are hyperelliptic):

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

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{43}$

The isogeny class factors as 1.43.f^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.ak_eh	$2$	(not in LMFDB)
2.43.a_cj	$2$	(not in LMFDB)
2.43.aba_jv	$3$	(not in LMFDB)
2.43.ai_v	$3$	(not in LMFDB)
2.43.af_as	$3$	(not in LMFDB)
2.43.n_ew	$3$	(not in LMFDB)
2.43.q_fu	$3$	(not in LMFDB)