Abelian variety isogeny class 2.157.abt_bfo over $\F_{157}$

• Label: 2.157.abt_bfo
• Base field: $\F_{157}$
• 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:	$\F_{157}$
Dimension:	$2$
L-polynomial:	$( 1 - 23 x + 157 x^{2} )( 1 - 22 x + 157 x^{2} )$
	$1 - 45 x + 820 x^{2} - 7065 x^{3} + 24649 x^{4}$
Frobenius angles:	$\pm0.129963694588$, $\pm0.158946998144$
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$18360$	$598168800$	$14969810724480$	$369159456201840000$	$9099133710986177947800$

Point counts of the (virtual) curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$113$	$24265$	$3868274$	$607596673$	$95389766333$	$14976085449670$	$2351243461615889$	$369145196578157473$	$57955795564432023578$	$9099059901098793613825$

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 $\F_{157}$.

Endomorphism algebra over $\F_{157}$

The isogeny class factors as 1.157.ax $\times$ 1.157.aw and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.157.ax : \(\Q(\sqrt{-11}) \).
• 1.157.aw : \(\Q(\sqrt{-1}) \).

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
2.157.ab_ahk	$2$	(not in LMFDB)
2.157.b_ahk	$2$	(not in LMFDB)
2.157.bt_bfo	$2$	(not in LMFDB)