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

• Label: 1.463.ai
• 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:	$1 - 8 x + 463 x^{2}$
Frobenius angles:	$\pm0.440481322678$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-447}) \)
Galois group:	$C_2$
Jacobians:	$28$
Isomorphism classes:	28

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$456$	$215232$	$99263448$	$45953753856$	$21276726136296$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$456$	$215232$	$99263448$	$45953753856$	$21276726136296$	$9851127723751104$	$4561072100336970744$	$2111776380538953796608$	$977752464190755881314824$	$452699390921217335710026432$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 28 curves (of which 0 are hyperelliptic):

• $y^2=x^3+87 x+261$
• $y^2=x^3+257 x+308$
• $y^2=x^3+181 x+80$
• $y^2=x^3+173 x+56$
• $y^2=x^3+195 x+195$
• $y^2=x^3+77 x+77$
• $y^2=x^3+77 x+231$
• $y^2=x^3+6 x+18$
• $y^2=x^3+104 x+104$
• $y^2=x^3+150 x+150$
• $y^2=x^3+431 x+431$
• $y^2=x^3+197 x+197$
• $y^2=x^3+190 x+190$
• $y^2=x^3+458 x+458$
• $y^2=x^3+325 x+49$
• $y^2=x^3+382 x+382$
• $y^2=x^3+335 x+79$
• $y^2=x^3+344 x+106$
• $y^2=x^3+263 x+263$
• $y^2=x^3+79 x+79$
• $y^2=x^3+462 x+462$
• $y^2=x^3+187 x+98$
• $y^2=x^3+345 x+109$
• $y^2=x^3+444 x+444$
• $y^2=x^3+117 x+351$
• $y^2=x^3+374 x+196$
• $y^2=x^3+49 x+147$
• $y^2=x^3+236 x+245$

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 \(\Q(\sqrt{-447}) \).

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.i	$2$	(not in LMFDB)