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

• Label: 2.73.abe_oe
• Base field: $\F_{73}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: yes
• Geometrically simple: yes
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{73}$
Dimension:	$2$
L-polynomial:	$1 - 30 x + 368 x^{2} - 2190 x^{3} + 5329 x^{4}$
Frobenius angles:	$\pm0.0650840807172$, $\pm0.217019455223$
Angle rank:	$2$ (numerical)
Number field:	4.0.201024.4
Galois group:	$D_{4}$
Jacobians:	$6$
Isomorphism classes:	6

This isogeny class is simple and geometrically 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$3478$	$27538804$	$151159364806$	$806530164455376$	$4297709478118732918$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$44$	$5166$	$388568$	$28400710$	$2073111944$	$151334417022$	$11047397195228$	$806460057203134$	$58871586357401564$	$4297625828028149886$

Jacobians and polarizations

This isogeny class contains the Jacobians of 6 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=58x^6+65x^5+29x^4+71x^3+70x^2+49x+45$
• $y^2=10x^5+68x^4+12x^3+42x^2+40x+30$
• $y^2=50x^6+5x^5+13x^4+30x^3+41x^2+14x+5$
• $y^2=52x^6+17x^5+72x^4+62x^3+62x^2+37x+3$
• $y^2=71x^6+40x^5+13x^4+56x^3+50x^2+10x+40$
• $y^2=24x^6+68x^5+35x^4+25x^3+23x^2+23x$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{73}$.

Endomorphism algebra over $\F_{73}$

The endomorphism algebra of this simple isogeny class is 4.0.201024.4.

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.be_oe	$2$	(not in LMFDB)