Abelian variety isogeny class 1.373.ak over $\F_{373}$

• Label: 1.373.ak
• Base field: $\F_{373}$
• 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:	$\F_{373}$
Dimension:	$1$
L-polynomial:	$1 - 10 x + 373 x^{2}$
Frobenius angles:	$\pm0.416643222583$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-87}) \)
Galois group:	$C_2$
Jacobians:	$24$
Isomorphism classes:	24

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$364$	$139776$	$51905308$	$19356739584$	$7220110541644$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$364$	$139776$	$51905308$	$19356739584$	$7220110541644$	$2693103168397824$	$1004527483765448188$	$374688750741778636800$	$139758904018927604698924$	$52130071199244557893710336$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 24 curves (of which 0 are hyperelliptic):

• $y^2=x^3+348 x+323$
• $y^2=x^3+211 x+49$
• $y^2=x^3+279 x+185$
• $y^2=x^3+148 x+296$
• $y^2=x^3+215 x+57$
• $y^2=x^3+317 x+317$
• $y^2=x^3+197 x+21$
• $y^2=x^3+168 x+336$
• $y^2=x^3+348 x+348$
• $y^2=x^3+272 x+272$
• $y^2=x^3+234 x+95$
• $y^2=x^3+157 x+157$
• $y^2=x^3+21 x+42$
• $y^2=x^3+232 x+232$
• $y^2=x^3+61 x+61$
• $y^2=x^3+281 x+281$
• $y^2=x^3+59 x+118$
• $y^2=x^3+127 x+127$
• $y^2=x^3+248 x+248$
• $y^2=x^3+32 x+64$
• $y^2=x^3+18 x+18$
• $y^2=x^3+350 x+327$
• $y^2=x^3+362 x+351$
• $y^2=x^3+17 x+34$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{373}$.

Endomorphism algebra over $\F_{373}$

The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-87}) \).

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
1.373.k	$2$	(not in LMFDB)