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

• Label: 2.73.abc_nc
• 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:	$1 - 28 x + 340 x^{2} - 2044 x^{3} + 5329 x^{4}$
Frobenius angles:	$\pm0.142062947302$, $\pm0.236464216789$
Angle rank:	$2$ (numerical)
Number field:	4.0.465152.1
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$3598$	$27855716$	$151519958254$	$806822874858896$	$4297900337682289198$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$46$	$5226$	$389494$	$28411014$	$2073204006$	$151335118506$	$11047402050430$	$806460090006078$	$58871586572816878$	$4297625829016273546$

Jacobians and polarizations

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

• $y^2=15x^6+44x^5+41x^4+54x^3+46x^2+66x+31$
• $y^2=39x^6+67x^5+66x^4+32x^3+6x^2+25x+5$
• $y^2=7x^6+36x^5+33x^4+28x^3+72x^2+47x+9$
• $y^2=14x^6+26x^5+7x^4+2x^3+63x^2+65x+20$
• $y^2=52x^6+30x^5+18x^4+59x^3+35x^2+9x+35$
• $y^2=20x^6+33x^5+7x^4+58x^3+16x+45$
• $y^2=19x^6+72x^5+40x^4+21x^3+25x^2+4x+28$
• $y^2=26x^6+72x^5+x^4+44x^3+70x^2+2x+36$
• $y^2=6x^6+15x^5+42x^4+29x^3+45x^2+49x+64$
• $y^2=12x^6+18x^5+8x^4+24x^3+37x^2+14x+43$
• $y^2=53x^6+23x^5+61x^4+52x^3+28x^2+10x+61$
• $y^2=8x^6+30x^5+48x^4+60x^3+27x^2+62x+38$

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 4.0.465152.1.

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_nc	$2$	(not in LMFDB)