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

• Label: 2.73.abb_mp
• 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:	$1 - 27 x + 327 x^{2} - 1971 x^{3} + 5329 x^{4}$
Frobenius angles:	$\pm0.173277117652$, $\pm0.242024654440$
Angle rank:	$2$ (numerical)
Number field:	4.0.271525.1
Galois group:	$D_{4}$
Jacobians:	$11$
Isomorphism classes:	11

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$3659$	$28009645$	$151681682531$	$806933924203525$	$4297947348358642544$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$47$	$5255$	$389909$	$28414923$	$2073226682$	$151335114815$	$11047399925609$	$806460056107603$	$58871586206922707$	$4297625825906699150$

Jacobians and polarizations

This isogeny class contains the Jacobians of 11 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=22x^6+35x^5+49x^4+10x^3+66x^2+44x+14$
• $y^2=28x^6+64x^5+37x^4+72x^3+13x^2+42x+63$
• $y^2=50x^6+23x^5+38x^4+9x^3+8x^2+67x+6$
• $y^2=35x^6+39x^5+18x^4+72x^3+51x^2+41x+5$
• $y^2=52x^6+26x^5+50x^4+34x^3+70x^2+19x+47$
• $y^2=71x^6+43x^5+46x^4+8x^3+54x^2+13x+51$
• $y^2=61x^6+7x^5+55x^4+42x^3+14x^2+28x+52$
• $y^2=8x^6+24x^5+59x^4+34x^3+44x^2+14x+48$
• $y^2=29x^6+18x^5+48x^4+50x^3+11$
• $y^2=13x^6+47x^5+69x^4+6x^3+x^2+41x+15$
• $y^2=69x^6+14x^5+49x^4+13x^3+48x^2+66x+11$

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 4.0.271525.1.

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_mp	$2$	(not in LMFDB)