Abelian variety isogeny class 2.73.abf_ow over $\F_{73}$

• Label: 2.73.abf_ow
• Base field: $\F_{73}$
• 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:	$\F_{73}$
Dimension:	$2$
L-polynomial:	$( 1 - 16 x + 73 x^{2} )( 1 - 15 x + 73 x^{2} )$
	$1 - 31 x + 386 x^{2} - 2263 x^{3} + 5329 x^{4}$
Frobenius angles:	$\pm0.114200251220$, $\pm0.159004799845$
Angle rank:	$2$ (numerical)
Jacobians:	$0$
Isomorphism classes:	3

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$3422$	$27410220$	$151069747328$	$806544627091200$	$4297818566709710222$

Point counts of the (virtual) curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$43$	$5141$	$388336$	$28401217$	$2073164563$	$151335423794$	$11047410122491$	$806460183897793$	$58871587295993008$	$4297625832286582661$

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 $\F_{73}$.

Endomorphism algebra over $\F_{73}$

The isogeny class factors as 1.73.aq $\times$ 1.73.ap and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.73.aq : \(\Q(\sqrt{-1}) \).
• 1.73.ap : \(\Q(\sqrt{-67}) \).

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
2.73.ab_adq	$2$	(not in LMFDB)
2.73.b_adq	$2$	(not in LMFDB)
2.73.bf_ow	$2$	(not in LMFDB)