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

• Label: 2.43.aba_jv
• 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: no

Invariants

Base field:	$\F_{43}$
Dimension:	$2$
L-polynomial:	$( 1 - 13 x + 43 x^{2} )^{2}$
	$1 - 26 x + 255 x^{2} - 1118 x^{3} + 1849 x^{4}$
Frobenius angles:	$\pm0.0421616081610$, $\pm0.0421616081610$
Angle rank:	$1$ (numerical)
Jacobians:	$0$

This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.

Newton polygon

This isogeny class is ordinary.

$p$-rank:	$2$
Slopes:	$[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$961$	$3122289$	$6239104144$	$11666398503321$	$21605860488041041$

Point counts of the (virtual) curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$18$	$1684$	$78468$	$3412420$	$146970198$	$6321140278$	$271817359650$	$11688193587844$	$502592578782684$	$21611482169939764$

Jacobians and polarizations

This isogeny class is principally polarizable, but does not contain a Jacobian.

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{43}$

The isogeny class factors as 1.43.an^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_adf	$2$	(not in LMFDB)
2.43.ba_jv	$2$	(not in LMFDB)
2.43.ai_v	$3$	(not in LMFDB)
2.43.af_as	$3$	(not in LMFDB)
2.43.k_eh	$3$	(not in LMFDB)
2.43.n_ew	$3$	(not in LMFDB)
2.43.q_fu	$3$	(not in LMFDB)