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

• Label: 2.73.abc_nb
• 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:	$1 - 28 x + 339 x^{2} - 2044 x^{3} + 5329 x^{4}$
Frobenius angles:	$\pm0.127660593299$, $\pm0.245090951450$
Angle rank:	$2$ (numerical)
Number field:	4.0.906768.1
Galois group:	$D_{4}$
Jacobians:	$10$
Isomorphism classes:	10

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$3597$	$27844377$	$151487122644$	$806772362753049$	$4297848675112538997$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$46$	$5224$	$389410$	$28409236$	$2073179086$	$151334875222$	$11047400632174$	$806460092198884$	$58871586754061746$	$4297625831743425784$

Jacobians and polarizations

This isogeny class contains the Jacobians of 10 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=26x^6+3x^5+25x^4+x^3+4x^2+35x+42$
• $y^2=46x^6+23x^5+52x^4+67x^3+43x^2+x+13$
• $y^2=18x^6+57x^5+39x^4+55x^3+x^2+12x+51$
• $y^2=56x^6+53x^5+49x^4+54x^3+71x^2+24x+11$
• $y^2=7x^6+25x^5+38x^3+36x^2+9x+53$
• $y^2=4x^6+32x^5+6x^4+19x^3+63x^2+17x+61$
• $y^2=36x^6+50x^5+10x^4+46x^3+5x^2+51x+34$
• $y^2=68x^6+70x^5+28x^4+36x^3+41x^2+8x+28$
• $y^2=43x^6+21x^5+20x^4+34x^3+30x^2+67x+44$
• $y^2=51x^6+34x^5+17x^4+15x^3+53x+21$

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 4.0.906768.1.

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_nb	$2$	(not in LMFDB)