Abelian variety isogeny class 2.139.abt_bee over $\F_{139}$

• Label: 2.139.abt_bee
• Base field: $\F_{139}$
• 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:	$\F_{139}$
Dimension:	$2$
L-polynomial:	$( 1 - 23 x + 139 x^{2} )( 1 - 22 x + 139 x^{2} )$
	$1 - 45 x + 784 x^{2} - 6255 x^{3} + 19321 x^{4}$
Frobenius angles:	$\pm0.0707251543800$, $\pm0.117174211439$
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$13806$	$364561236$	$7201681820424$	$139343158506468384$	$2692448012954737577826$

Point counts of the (virtual) curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$95$	$18865$	$2681570$	$373272889$	$51888763925$	$7212551347186$	$1002544420941095$	$139353668097132529$	$19370159754758019110$	$2692452204348871439425$

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 $\F_{139}$.

Endomorphism algebra over $\F_{139}$

The isogeny class factors as 1.139.ax $\times$ 1.139.aw and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.139.ax : \(\Q(\sqrt{-3}) \).
• 1.139.aw : \(\Q(\sqrt{-2}) \).

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
2.139.ab_aiu	$2$	(not in LMFDB)
2.139.b_aiu	$2$	(not in LMFDB)
2.139.bt_bee	$2$	(not in LMFDB)
2.139.ap_eu	$3$	(not in LMFDB)
2.139.ag_acw	$3$	(not in LMFDB)