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

• Label: 2.73.abe_oh
• 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: yes

Invariants

Base field:	$\F_{73}$
Dimension:	$2$
L-polynomial:	$( 1 - 15 x + 73 x^{2} )^{2}$
	$1 - 30 x + 371 x^{2} - 2190 x^{3} + 5329 x^{4}$
Frobenius angles:	$\pm0.159004799845$, $\pm0.159004799845$
Angle rank:	$1$ (numerical)
Jacobians:	$3$
Cyclic group of points:	no
Non-cyclic primes:	$59$

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

Newton polygon

This isogeny class is ordinary.

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

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$3481$	$27573001$	$151264989184$	$806711038270281$	$4297927782030847561$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$44$	$5172$	$388838$	$28407076$	$2073217244$	$151335766158$	$11047410984668$	$806460166467268$	$58871586916879094$	$4297625827388882772$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 3 curves (of which all are hyperelliptic):

• $y^2=47 x^6+61 x^5+69 x^4+28 x^3+54 x^2+3 x+40$
• $y^2=39 x^6+68 x^5+64 x^4+27 x^3+51 x^2+51 x+2$
• $y^2=18 x^6+67 x^5+34 x^4+20 x^3+24 x^2+60 x+59$

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^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-67}) \)$)$

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.a_adb	$2$	(not in LMFDB)
2.73.be_oh	$2$	(not in LMFDB)
2.73.p_fw	$3$	(not in LMFDB)