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

• Label: 2.73.abd_nr
• 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:	$1 - 29 x + 355 x^{2} - 2117 x^{3} + 5329 x^{4}$
Frobenius angles:	$\pm0.132995750451$, $\pm0.213626865826$
Angle rank:	$2$ (numerical)
Number field:	4.0.135725.2
Galois group:	$D_{4}$
Jacobians:	$4$
Isomorphism classes:	4

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$3539$	$27713909$	$151391203979$	$806762117422421$	$4297903828472423664$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$45$	$5199$	$389163$	$28408875$	$2073205690$	$151335345423$	$11047405107231$	$806460112875699$	$58871586632554569$	$4297625828042614414$

Jacobians and polarizations

This isogeny class contains the Jacobians of 4 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=54x^6+13x^5+8x^4+42x^3+7x^2+43x+47$
• $y^2=52x^6+27x^5+12x^4+22x^3+72x^2+16x+22$
• $y^2=58x^6+9x^5+8x^4+64x^3+30x^2+30x+51$
• $y^2=11x^6+59x^5+29x^4+72x^3+65x^2+53x+45$

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 4.0.135725.2.

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.bd_nr	$2$	(not in LMFDB)