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

• Label: 2.73.abi_qt
• 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:	$( 1 - 17 x + 73 x^{2} )^{2}$
	$1 - 34 x + 435 x^{2} - 2482 x^{3} + 5329 x^{4}$
Frobenius angles:	$\pm0.0323195869136$, $\pm0.0323195869136$
Angle rank:	$1$ (numerical)
Jacobians:	$0$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$3249$	$26904969$	$150410557584$	$805904150179401$	$4297295902545728289$

Point counts of the (virtual) curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$40$	$5044$	$386638$	$28378660$	$2072912440$	$151332950158$	$11047388443096$	$806460013759684$	$58871586115531294$	$4297625825330846164$

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.ar^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-3}) \)$)$

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
2.73.a_afn	$2$	(not in LMFDB)
2.73.bi_qt	$2$	(not in LMFDB)
2.73.ak_bb	$3$	(not in LMFDB)
2.73.ah_ay	$3$	(not in LMFDB)
2.73.o_hn	$3$	(not in LMFDB)
2.73.r_ii	$3$	(not in LMFDB)
2.73.u_jm	$3$	(not in LMFDB)