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

• Label: 1.373.ax
• 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:	$1 - 23 x + 373 x^{2}$
Frobenius angles:	$\pm0.296974806244$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-107}) \)
Galois group:	$C_2$
Jacobians:	$9$
Isomorphism classes:	9

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$351$	$139347$	$51908688$	$19357109811$	$7220115988371$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$351$	$139347$	$51908688$	$19357109811$	$7220115988371$	$2693103088089024$	$1004527479886120359$	$374688750707676657603$	$139758904019842144646544$	$52130071199271443880466107$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 9 curves (of which 0 are hyperelliptic):

• $y^2=x^3+120 x+120$
• $y^2=x^3+362 x+362$
• $y^2=x^3+152 x+304$
• $y^2=x^3+209 x+45$
• $y^2=x^3+207 x+207$
• $y^2=x^3+126 x+252$
• $y^2=x^3+353 x+333$
• $y^2=x^3+349 x+325$
• $y^2=x^3+306 x+239$

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 \(\Q(\sqrt{-107}) \).

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.x	$2$	(not in LMFDB)