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

• Label: 2.73.abc_my
• 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:	$1 - 28 x + 336 x^{2} - 2044 x^{3} + 5329 x^{4}$
Frobenius angles:	$\pm0.0872906235122$, $\pm0.263736764141$
Angle rank:	$2$ (numerical)
Number field:	4.0.1956096.1
Galois group:	$D_{4}$
Jacobians:	$12$
Isomorphism classes:	12

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$3594$	$27810372$	$151388627994$	$806620150116624$	$4297690205981945274$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$46$	$5218$	$389158$	$28403878$	$2073102646$	$151334085058$	$11047394905054$	$806460071590846$	$58871586899941774$	$4297625835257832418$

Jacobians and polarizations

This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=31x^6+42x^5+50x^4+47x^3+27x^2+14x+10$
• $y^2=5x^6+10x^5+47x^4+2x^3+54x^2+58x+10$
• $y^2=13x^6+37x^5+53x^4+10x^3+14x^2+59x+16$
• $y^2=68x^6+18x^5+43x^4+19x^3+26x^2+42x+8$
• $y^2=60x^6+25x^5+10x^4+21x^3+63x^2+42x+33$
• $y^2=65x^6+22x^5+38x^4+58x^3+26x^2+46x+7$
• $y^2=17x^6+x^5+59x^4+51x^3+57x^2+62x+5$
• $y^2=56x^6+5x^5+67x^4+4x^3+23x^2+42x+34$
• $y^2=60x^6+66x^5+58x^4+16x^3+30x^2+72x+70$
• $y^2=20x^6+13x^5+47x^4+21x^3+29x^2+64x+3$
• $y^2=68x^6+22x^5+39x^4+39x^3+24x^2+55x+35$
• $y^2=37x^6+14x^5+4x^4+34x^3+61x^2+71x$

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 4.0.1956096.1.

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.bc_my	$2$	(not in LMFDB)