Abelian variety isogeny class 2.199.acd_bsk over $\F_{199}$

• Label: 2.199.acd_bsk
• Base field: $\F_{199}$
• 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:	$\F_{199}$
Dimension:	$2$
L-polynomial:	$( 1 - 28 x + 199 x^{2} )( 1 - 27 x + 199 x^{2} )$
	$1 - 55 x + 1154 x^{2} - 10945 x^{3} + 39601 x^{4}$
Frobenius angles:	$\pm0.0391815390403$, $\pm0.0936959350875$
Angle rank:	$2$ (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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$29756$	$1540051536$	$62034525741104$	$2459217132947674944$	$97393358188810034661476$

Point counts of the (virtual) curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$145$	$38885$	$7871800$	$1568139049$	$312078578275$	$62103832003406$	$12358664238953485$	$2459374192033203889$	$489415464138299521000$	$97393677360098926549325$

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 $\F_{199}$.

Endomorphism algebra over $\F_{199}$

The isogeny class factors as 1.199.abc $\times$ 1.199.abb and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.199.abc : \(\Q(\sqrt{-3}) \).
• 1.199.abb : \(\Q(\sqrt{-67}) \).

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
2.199.ab_anu	$2$	(not in LMFDB)
2.199.b_anu	$2$	(not in LMFDB)
2.199.cd_bsk	$2$	(not in LMFDB)
2.199.aq_dx	$3$	(not in LMFDB)
2.199.ak_acj	$3$	(not in LMFDB)