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

• Label: 2.73.abd_ns
• 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:	$( 1 - 15 x + 73 x^{2} )( 1 - 14 x + 73 x^{2} )$
	$1 - 29 x + 356 x^{2} - 2117 x^{3} + 5329 x^{4}$
Frobenius angles:	$\pm0.159004799845$, $\pm0.194368965322$
Angle rank:	$2$ (numerical)
Jacobians:	$0$
Isomorphism classes:	6

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$3540$	$27725280$	$151425227520$	$806817292617600$	$4297964851926203700$

Point counts of the (virtual) curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$45$	$5201$	$389250$	$28410817$	$2073235125$	$151335670574$	$11047407571245$	$806460119424193$	$58871586470169330$	$4297625824464784961$

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.ap $\times$ 1.73.ao 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.ap : \(\Q(\sqrt{-67}) \).
• 1.73.ao : \(\Q(\sqrt{-6}) \).

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
2.73.ab_acm	$2$	(not in LMFDB)
2.73.b_acm	$2$	(not in LMFDB)
2.73.bd_ns	$2$	(not in LMFDB)