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

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

Invariants

Base field:	$\F_{43}$
Dimension:	$2$
L-polynomial:	$1 - 6 x - 7 x^{2} - 258 x^{3} + 1849 x^{4}$
Frobenius angles:	$\pm0.0154131777858$, $\pm0.682079844452$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-3}, \sqrt{-34})\)
Galois group:	$C_2^2$
Jacobians:	$0$
Isomorphism classes:	12

This isogeny class is simple but not geometrically simple, primitive, ordinary, and not supersingular.

Newton polygon

This isogeny class is ordinary.

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

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$1579$	$3326953$	$6233102500$	$11684102569209$	$21609011824807579$

Point counts of the (virtual) curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$38$	$1800$	$78392$	$3417604$	$146991638$	$6321058350$	$271818419666$	$11688194875204$	$502592530644056$	$21611482301709000$

Jacobians and polarizations

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

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 \(\Q(\sqrt{-3}, \sqrt{-34})\).

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

The base change of $A$ to $\F_{43^{3}}$ is 1.79507.avm^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-34}) \)$)$

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.g_ah	$2$	(not in LMFDB)
2.43.m_es	$3$	(not in LMFDB)
2.43.am_es	$6$	(not in LMFDB)