Abelian variety isogeny class 1.383.aq over $\F_{383}$

• Label: 1.383.aq
• Base field: $\F_{383}$
• 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:	$\F_{383}$
Dimension:	$1$
L-polynomial:	$1 - 16 x + 383 x^{2}$
Frobenius angles:	$\pm0.365954021716$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-319}) \)
Galois group:	$C_2$
Jacobians:	$20$
Isomorphism classes:	20

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$368$	$147200$	$56196176$	$21517696000$	$8241259882288$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$368$	$147200$	$56196176$	$21517696000$	$8241259882288$	$3156404335097600$	$1208902895918768656$	$463009809016641024000$	$177332756837823797562608$	$67918445868683773775456000$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 20 curves (of which 0 are hyperelliptic):

• $y^2=x^3+346 x+198$
• $y^2=x^3+5 x+5$
• $y^2=x^3+29 x+145$
• $y^2=x^3+256 x+256$
• $y^2=x^3+68 x+68$
• $y^2=x^3+119 x+119$
• $y^2=x^3+103 x+132$
• $y^2=x^3+221 x+221$
• $y^2=x^3+114 x+187$
• $y^2=x^3+85 x+85$
• $y^2=x^3+375 x+343$
• $y^2=x^3+242 x+242$
• $y^2=x^3+187 x+169$
• $y^2=x^3+289 x+289$
• $y^2=x^3+54 x+54$
• $y^2=x^3+313 x+33$
• $y^2=x^3+27 x+135$
• $y^2=x^3+347 x+203$
• $y^2=x^3+115 x+115$
• $y^2=x^3+251 x+106$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{383}$.

Endomorphism algebra over $\F_{383}$

The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-319}) \).

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
1.383.q	$2$	(not in LMFDB)