Abelian variety isogeny class 1.181.at over $\F_{181}$

• Label: 1.181.at
• Base field: $\F_{181}$
• 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:	$\F_{181}$
Dimension:	$1$
L-polynomial:	$1 - 19 x + 181 x^{2}$
Frobenius angles:	$\pm0.250439655098$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-3}) \)
Galois group:	$C_2$
Jacobians:	$5$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$163$	$32763$	$5933200$	$1073348643$	$194264863903$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$163$	$32763$	$5933200$	$1073348643$	$194264863903$	$35161828228800$	$6364290813295123$	$1151936655677065443$	$208500535045888430800$	$37738596846961070751603$

Jacobians and polarizations

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

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{181}$.

Endomorphism algebra over $\F_{181}$

The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-3}) \).

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

Twist	Extension degree	Common base change
1.181.t	$2$	(not in LMFDB)
1.181.ah	$3$	(not in LMFDB)
1.181.ba	$3$	(not in LMFDB)