Abelian variety isogeny class 2.1024.aev_iuy over $\F_{2^{10}}$

• Label: 2.1024.aev_iuy
• Base field: $\F_{2^{10}}$
• Dimension: $2$
• $p$-rank: $1$
• Ordinary: no
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: no

Invariants

Base field:	$\F_{2^{10}}$
Dimension:	$2$
L-polynomial:	$( 1 - 32 x )^{2}( 1 - 61 x + 1024 x^{2} )$
	$1 - 125 x + 5952 x^{2} - 128000 x^{3} + 1048576 x^{4}$
Frobenius angles:	$0$, $0$, $\pm0.0978468837242$
Angle rank:	$1$ (numerical)

This isogeny class is not simple, primitive, not ordinary, and not supersingular. It is principally polarizable.

Newton polygon

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

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$926404$	$1095615396216$	$1152808632239482204$	$1208922742163319108750000$	$1267650522115407331168052142004$

Point counts of the (virtual) curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$900$	$1044856$	$1073636700$	$1099508828848$	$1125899837464500$	$1152921503039558056$	$1180591620686407428300$	$1208925819614136683748448$	$1237940039285375383849064100$	$1267650600228229396347157719256$

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 $\F_{2^{10}}$.

Endomorphism algebra over $\F_{2^{10}}$

The isogeny class factors as 1.1024.acm $\times$ 1.1024.acj and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.1024.acm : the quaternion algebra over \(\Q\) ramified at $2$ and $\infty$.
• 1.1024.acj : \(\Q(\sqrt{-15}) \).

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
2.1024.ad_actk	$2$	(not in LMFDB)
2.1024.d_actk	$2$	(not in LMFDB)
2.1024.ev_iuy	$2$	(not in LMFDB)
2.1024.abd_ds	$3$	(not in LMFDB)