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

• Label: 2.73.abb_mh
• 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:	$1 - 27 x + 319 x^{2} - 1971 x^{3} + 5329 x^{4}$
Frobenius angles:	$\pm0.0807289326480$, $\pm0.290347381756$
Angle rank:	$2$ (numerical)
Number field:	4.0.4595733.2
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$3651$	$27919197$	$151428499947$	$806564857366629$	$4297598070901537776$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$47$	$5239$	$389261$	$28401931$	$2073058202$	$151333651807$	$11047393256177$	$806460087000979$	$58871587194085907$	$4297625837069745934$

Jacobians and polarizations

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

• $y^2=43x^6+53x^5+52x^4+19x^3+28x^2+32x+51$
• $y^2=39x^6+13x^5+58x^4+6x^2+6x+7$
• $y^2=7x^6+6x^5+14x^4+61x^3+43x^2+31x+44$
• $y^2=20x^6+16x^5+72x^4+57x^3+71x^2+43x+43$
• $y^2=44x^6+33x^5+9x^4+13x^3+36x^2+63x+50$
• $y^2=39x^6+44x^4+37x^3+59x^2+66x+27$
• $y^2=33x^6+69x^5+32x^4+50x^3+33x^2+54x+31$
• $y^2=12x^6+40x^5+63x^4+8x^3+10x^2+44x+59$
• $y^2=29x^6+66x^5+23x^4+52x^3+24x^2+5x+40$
• $y^2=42x^6+6x^5+5x^4+32x^3+37x^2+9x+63$
• $y^2=52x^6+28x^5+14x^4+59x^3+30x^2+61x+41$
• $y^2=34x^6+41x^5+15x^4+50x^3+30x^2+61x+40$

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 4.0.4595733.2.

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.bb_mh	$2$	(not in LMFDB)