Abelian variety isogeny class 1.83.ae over $\F_{83}$

• Label: 1.83.ae
• Base field: $\F_{83}$
• 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:	$\F_{83}$
Dimension:	$1$
L-polynomial:	$1 - 4 x + 83 x^{2}$
Frobenius angles:	$\pm0.429548098763$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-79}) \)
Galois group:	$C_2$
Jacobians:	$10$
Isomorphism classes:	10

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$80$	$7040$	$572720$	$47449600$	$3938928400$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$80$	$7040$	$572720$	$47449600$	$3938928400$	$326940648320$	$27136061405680$	$2252292250982400$	$186940254478381520$	$15516041182485219200$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 10 curves (of which 0 are hyperelliptic):

• $y^2=x^3+7 x+14$
• $y^2=x^3+51 x+51$
• $y^2=x^3+59 x+59$
• $y^2=x^3+38 x+38$
• $y^2=x^3+34 x+68$
• $y^2=x^3+53 x+23$
• $y^2=x^3+62 x+62$
• $y^2=x^3+72 x+61$
• $y^2=x^3+55 x+27$
• $y^2=x^3+24 x+24$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{83}$.

Endomorphism algebra over $\F_{83}$

The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-79}) \).

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
1.83.e	$2$	(not in LMFDB)