Abelian variety isogeny class 2.79.az_mc over $\F_{79}$

• Label: 2.79.az_mc
• Base field: $\F_{79}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: no

Invariants

Base field:	$\F_{79}$
Dimension:	$2$
L-polynomial:	$( 1 - 13 x + 79 x^{2} )( 1 - 12 x + 79 x^{2} )$
	$1 - 25 x + 314 x^{2} - 1975 x^{3} + 6241 x^{4}$
Frobenius angles:	$\pm0.238910621905$, $\pm0.264120855861$
Angle rank:	$2$ (numerical)
Jacobians:	$0$
Cyclic group of points:	no
Non-cyclic primes:	$2$

This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.

Newton polygon

This isogeny class is ordinary.

$p$-rank:	$2$
Slopes:	$[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$4556$	$38981136$	$244075508144$	$1518069042345024$	$9468738037257922676$

Point counts of the (virtual) curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$55$	$6245$	$495040$	$38974729$	$3077206525$	$243087400766$	$19203896673835$	$1517108661966769$	$119851595105120320$	$9468276083167382525$

Jacobians and polarizations

This isogeny class is principally polarizable, but does not contain a Jacobian.

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{79}$

The isogeny class factors as 1.79.an $\times$ 1.79.am and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.79.an : \(\Q(\sqrt{-3}) \).
• 1.79.am : \(\Q(\sqrt{-43}) \).

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
2.79.ab_c	$2$	(not in LMFDB)
2.79.b_c	$2$	(not in LMFDB)
2.79.z_mc	$2$	(not in LMFDB)
2.79.aq_hy	$3$	(not in LMFDB)
2.79.f_abu	$3$	(not in LMFDB)