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

• Label: 2.73.abb_mf
• 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:	$1 - 27 x + 317 x^{2} - 1971 x^{3} + 5329 x^{4}$
Frobenius angles:	$\pm0.0527273925472$, $\pm0.297649276576$
Angle rank:	$2$ (numerical)
Number field:	4.0.37525.1
Galois group:	$D_{4}$
Jacobians:	$18$
Isomorphism classes:	18

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$3649$	$27896605$	$151365223561$	$806471462409525$	$4297505155999078144$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$47$	$5235$	$389099$	$28398643$	$2073013382$	$151333193355$	$11047389441779$	$806460057374083$	$58871586928034927$	$4297625834193221550$

Jacobians and polarizations

This isogeny class contains the Jacobians of 18 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=5x^6+22x^5+12x^4+59x^3+39x^2+11x+50$
• $y^2=65x^6+65x^5+50x^4+23x^3+67x^2+48x+37$
• $y^2=63x^6+22x^5+43x^4+29x^3+57x^2+17x+39$
• $y^2=13x^6+57x^5+30x^4+46x^3+43x^2+69x+34$
• $y^2=38x^6+45x^5+45x^4+30x^3+11x^2+11x+32$
• $y^2=28x^6+15x^5+67x^4+53x^3+10x^2+67x+10$
• $y^2=25x^6+5x^5+2x^4+65x^3+65x^2+2x+22$
• $y^2=46x^6+46x^5+9x^4+60x^3+27x^2+26x+34$
• $y^2=51x^6+67x^5+65x^4+42x^3+4x^2+57x+26$
• $y^2=33x^6+61x^5+44x^4+53x^3+60x^2+39x+68$
• $y^2=38x^6+17x^5+17x^4+44x^3+14x^2+21x+46$
• $y^2=58x^6+61x^5+35x^4+55x^3+38x^2+15x+42$
• $y^2=67x^5+24x^4+3x^3+37x^2+16x+68$
• $y^2=56x^6+52x^5+x^4+35x^3+38x^2+44x+22$
• $y^2=47x^6+50x^5+58x^4+7x^3+34x^2+51x+56$
• $y^2=40x^6+72x^5+46x^4+47x^3+55x^2+55x+62$
• $y^2=36x^6+39x^5+67x^4+4x^3+41x^2+27x+57$
• $y^2=66x^6+66x^5+23x^4+47x^3+69x^2+7x+56$

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 4.0.37525.1.

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.bb_mf	$2$	(not in LMFDB)