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

• Label: 1.373.av
• 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:	$1 - 21 x + 373 x^{2}$
Frobenius angles:	$\pm0.317034548098$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-1051}) \)
Galois group:	$C_2$
Jacobians:	$5$
Isomorphism classes:	5

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$353$	$139435$	$51909356$	$19357063875$	$7220114312213$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$353$	$139435$	$51909356$	$19357063875$	$7220114312213$	$2693103069513280$	$1004527480281946001$	$374688750726804499875$	$139758904020125637068348$	$52130071199269490143996675$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 5 curves (of which 0 are hyperelliptic):

• $y^2=x^3+252 x+252$
• $y^2=x^3+319 x+319$
• $y^2=x^3+321 x+321$
• $y^2=x^3+136 x+136$
• $y^2=x^3+311 x+311$

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 \(\Q(\sqrt{-1051}) \).

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.v	$2$	(not in LMFDB)