Abelian variety isogeny class 1.79.i over $\F_{79}$

• Label: 1.79.i
• Base field: $\F_{79}$
• 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:	$\F_{79}$
Dimension:	$1$
L-polynomial:	$1 + 8 x + 79 x^{2}$
Frobenius angles:	$\pm0.648588554586$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-7}) \)
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$88$	$6336$	$491656$	$38953728$	$3077136568$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$88$	$6336$	$491656$	$38953728$	$3077136568$	$243086526144$	$19203910087912$	$1517108874513408$	$119851595378725144$	$9468276082354051776$

Jacobians and polarizations

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

• $y^2=x^3+26 x+78$
• $y^2=x^3+41 x+44$
• $y^2=x^3+30 x+11$
• $y^2=x^3+5 x+5$
• $y^2=x^3+6 x+6$
• $y^2=x^3+59 x+59$
• $y^2=x^3+74 x+64$
• $y^2=x^3+10 x+10$
• $y^2=x^3+4 x+4$
• $y^2=x^3+50 x+50$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{79}$.

Endomorphism algebra over $\F_{79}$

The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-7}) \).

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
1.79.ai	$2$	(not in LMFDB)