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

• Label: 1.463.ag
• 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:	$1 - 6 x + 463 x^{2}$
Frobenius angles:	$\pm0.455475605178$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-454}) \)
Galois group:	$C_2$
Jacobians:	$14$
Isomorphism classes:	14

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$458$	$215260$	$99260966$	$45953704800$	$21276727619738$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$458$	$215260$	$99260966$	$45953704800$	$21276727619738$	$9851127770209180$	$4561072099756594166$	$2111776380505710115200$	$977752464190838893832618$	$452699390921237156058694300$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 14 curves (of which 0 are hyperelliptic):

• $y^2=x^3+187 x+187$
• $y^2=x^3+385 x+385$
• $y^2=x^3+240 x+257$
• $y^2=x^3+132 x+396$
• $y^2=x^3+10 x+10$
• $y^2=x^3+412 x+310$
• $y^2=x^3+334 x+76$
• $y^2=x^3+462 x+460$
• $y^2=x^3+211 x+170$
• $y^2=x^3+216 x+185$
• $y^2=x^3+420 x+420$
• $y^2=x^3+339 x+339$
• $y^2=x^3+86 x+86$
• $y^2=x^3+338 x+88$

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 \(\Q(\sqrt{-454}) \).

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.g	$2$	(not in LMFDB)