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

• Label: 2.157.aby_bkd
• 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:	$( 1 - 25 x + 157 x^{2} )^{2}$
	$1 - 50 x + 939 x^{2} - 7850 x^{3} + 24649 x^{4}$
Frobenius angles:	$\pm0.0220179720414$, $\pm0.0220179720414$
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$17689$	$592386921$	$14946296209936$	$369087572149556841$	$9098949035711285113489$

Point counts of the (virtual) curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$108$	$24028$	$3862194$	$607478356$	$95387830308$	$14976057666022$	$2351243105875044$	$369145192505797348$	$57955795523282943258$	$9099059900745544837228$

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.az^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
2.157.a_alz	$2$	(not in LMFDB)
2.157.by_bkd	$2$	(not in LMFDB)
2.157.ao_bn	$3$	(not in LMFDB)
2.157.al_abk	$3$	(not in LMFDB)
2.157.w_qt	$3$	(not in LMFDB)
2.157.z_sa	$3$	(not in LMFDB)
2.157.bc_tq	$3$	(not in LMFDB)