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

• Label: 1.463.aq
• 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:	$1 - 16 x + 463 x^{2}$
Frobenius angles:	$\pm0.378743621829$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-399}) \)
Galois group:	$C_2$
Jacobians:	$32$
Isomorphism classes:	32

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$448$	$215040$	$99270976$	$45954048000$	$21276724842688$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$448$	$215040$	$99270976$	$45954048000$	$21276724842688$	$9851127507486720$	$4561072098164846656$	$2111776380637335552000$	$977752464193280641851328$	$452699390921196459329587200$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 32 curves (of which 0 are hyperelliptic):

• $y^2=x^3+369 x+181$
• $y^2=x^3+430 x+364$
• $y^2=x^3+29 x+29$
• $y^2=x^3+274 x+274$
• $y^2=x^3+7 x+7$
• $y^2=x^3+146 x+146$
• $y^2=x^3+406 x+406$
• $y^2=x^3+280 x+377$
• $y^2=x^3+439 x+391$
• $y^2=x^3+295 x+295$
• $y^2=x^3+118 x+354$
• $y^2=x^3+429 x+361$
• $y^2=x^3+5 x+5$
• $y^2=x^3+272 x+353$
• $y^2=x^3+310 x+310$
• $y^2=x^3+204 x+204$
• $y^2=x^3+326 x+52$
• $y^2=x^3+191 x+110$
• $y^2=x^3+229 x+229$
• $y^2=x^3+179 x+74$
• and

• $y^2=x^3+456 x+456$
• $y^2=x^3+213 x+176$
• $y^2=x^3+241 x+260$
• $y^2=x^3+46 x+138$
• $y^2=x^3+32 x+32$
• $y^2=x^3+61 x+61$
• $y^2=x^3+325 x+325$
• $y^2=x^3+81 x+81$
• $y^2=x^3+362 x+160$
• $y^2=x^3+219 x+219$
• $y^2=x^3+64 x+192$
• $y^2=x^3+415 x+319$

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 \(\Q(\sqrt{-399}) \).

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.q	$2$	(not in LMFDB)