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

• Label: 1.79.e
• 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:	$1 + 4 x + 79 x^{2}$
Frobenius angles:	$\pm0.572243955238$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-3}) \)
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$84$	$6384$	$492156$	$38942400$	$3077156964$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$84$	$6384$	$492156$	$38942400$	$3077156964$	$243087660144$	$19203900223116$	$1517108828793600$	$119851596599350644$	$9468276078667841904$

Jacobians and polarizations

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

• $y^2=x^3+18 x+18$
• $y^2=x^3+61 x+61$
• $y^2=x^3+56 x+10$
• $y^2=x^3+63 x+63$
• $y^2=x^3+15 x+45$
• $y^2=x^3+23 x+69$
• $y^2=x^3+36 x+36$
• $y^2=x^3+1$
• $y^2=x^3+x+3$
• $y^2=x^3+24 x+24$

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 \(\Q(\sqrt{-3}) \).

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
1.79.ae	$2$	(not in LMFDB)
1.79.ar	$3$	(not in LMFDB)
1.79.n	$3$	(not in LMFDB)