Abelian variety isogeny class 1.431.abb over $\F_{431}$

• Label: 1.431.abb
• Base field: $\F_{431}$
• 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:	$\F_{431}$
Dimension:	$1$
L-polynomial:	$1 - 27 x + 431 x^{2}$
Frobenius angles:	$\pm0.274654880019$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-995}) \)
Galois group:	$C_2$
Jacobians:	$8$
Isomorphism classes:	8

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$405$	$185895$	$80078220$	$34507502955$	$14872584261375$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$405$	$185895$	$80078220$	$34507502955$	$14872584261375$	$6410082456100080$	$2762745566283812745$	$1190743340402747578995$	$513210379737672945759780$	$221193673667012298713817375$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 8 curves (of which 0 are hyperelliptic):

• $y^2=x^3+178 x+384$
• $y^2=x^3+403 x+235$
• $y^2=x^3+294 x+334$
• $y^2=x^3+142 x+132$
• $y^2=x^3+378 x+60$
• $y^2=x^3+262 x+262$
• $y^2=x^3+98 x+98$
• $y^2=x^3+25 x+25$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{431}$.

Endomorphism algebra over $\F_{431}$

The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-995}) \).

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
1.431.bb	$2$	(not in LMFDB)