Abelian variety isogeny class 1.263.abe over $\F_{263}$

• Label: 1.263.abe
• Base field: $\F_{263}$
• Dimension: $1$
• $p$-rank: $1$
• Ordinary: yes
• Supersingular: no
• Simple: yes
• Geometrically simple: yes
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{263}$
Dimension:	$1$
L-polynomial:	$1 - 30 x + 263 x^{2}$
Frobenius angles:	$\pm0.124115263538$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-38}) \)
Galois group:	$C_2$
Jacobians:	$6$

This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

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

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$234$	$68796$	$18188118$	$4784349024$	$1258285027194$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$234$	$68796$	$18188118$	$4784349024$	$1258285027194$	$330928769247804$	$87034260200473638$	$22890010300107350400$	$6020072706557093390154$	$1583279121788259696509436$

Jacobians and polarizations

This isogeny class contains the Jacobians of 6 curves (of which all are hyperelliptic), and hence is principally polarizable:

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{263}$.

Endomorphism algebra over $\F_{263}$

The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-38}) \).

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.

Twist	Extension degree	Common base change
1.263.be	$2$	(not in LMFDB)