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

• Label: 1.373.ar
• 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:	$1 - 17 x + 373 x^{2}$
Frobenius angles:	$\pm0.354938269793$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-1203}) \)
Galois group:	$C_2$
Jacobians:	$6$
Isomorphism classes:	6

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$357$	$139587$	$51909228$	$19356948051$	$7220111650017$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$357$	$139587$	$51909228$	$19356948051$	$7220111650017$	$2693103073141824$	$1004527481732351997$	$374688750756298154883$	$139758904020068417795004$	$52130071199254837529024907$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 6 curves (of which 0 are hyperelliptic):

• $y^2=x^3+339 x+305$
• $y^2=x^3+3 x+3$
• $y^2=x^3+356 x+339$
• $y^2=x^3+28 x+56$
• $y^2=x^3+334 x+295$
• $y^2=x^3+37 x+74$

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 \(\Q(\sqrt{-1203}) \).

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.r	$2$	(not in LMFDB)