Abelian variety isogeny class 1.463.abb over $\F_{463}$

• Label: 1.463.abb
• Base field: $\F_{463}$
• 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:	$\F_{463}$
Dimension:	$1$
L-polynomial:	$1 - 27 x + 463 x^{2}$
Frobenius angles:	$\pm0.284119851477$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-1123}) \)
Galois group:	$C_2$
Jacobians:	$5$
Isomorphism classes:	5

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$437$	$214567$	$99270668$	$45954458091$	$21276735835967$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$437$	$214567$	$99270668$	$45954458091$	$21276735835967$	$9851127518558704$	$4561072091942596457$	$2111776380485697433203$	$977752464193073832416804$	$452699390921267238819879007$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 5 curves (of which 0 are hyperelliptic):

• $y^2=x^3+108 x+324$
• $y^2=x^3+289 x+404$
• $y^2=x^3+427 x+355$
• $y^2=x^3+323 x+323$
• $y^2=x^3+250 x+250$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{463}$.

Endomorphism algebra over $\F_{463}$

The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-1123}) \).

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
1.463.bb	$2$	(not in LMFDB)