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

• Label: 2.73.abc_mw
• 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:	$1 - 28 x + 334 x^{2} - 2044 x^{3} + 5329 x^{4}$
Frobenius angles:	$\pm0.0555528882213$, $\pm0.273187710002$
Angle rank:	$2$ (numerical)
Number field:	4.0.23552.1
Galois group:	$D_{4}$
Jacobians:	$14$
Isomorphism classes:	22

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$3592$	$27787712$	$151322974984$	$806518111345664$	$4297581658660955272$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$46$	$5214$	$388990$	$28400286$	$2073050286$	$151333507902$	$11047389848254$	$806460034606014$	$58871586645429166$	$4297625833183371934$

Jacobians and polarizations

This isogeny class contains the Jacobians of 14 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=28x^6+18x^5+54x^4+17x^3+3x^2+8x+21$
• $y^2=7x^6+30x^5+20x^4+72x^3+10x^2+21x+33$
• $y^2=61x^6+19x^5+14x^4+24x^3+58x^2+71x+28$
• $y^2=40x^6+x^5+68x^4+11x^3+55x^2+6x+40$
• $y^2=45x^6+58x^5+40x^4+28x^3+8x^2+52x+66$
• $y^2=20x^6+68x^5+60x^4+48x^3+62x^2+67x+20$
• $y^2=29x^6+28x^5+36x^4+48x^3+53x^2+13x+51$
• $y^2=51x^6+45x^5+41x^4+8x^3+16x^2+60x+27$
• $y^2=7x^6+37x^5+21x^4+43x^3+28x^2+61x+22$
• $y^2=19x^6+9x^5+9x^4+17x^3+26x^2+18x+21$
• $y^2=51x^6+44x^5+64x^4+26x^3+13x^2+x+26$
• $y^2=57x^6+69x^5+39x^4+6x^3+71x^2+71x+39$
• $y^2=26x^6+29x^5+58x^4+38x^3+54x^2+60x+42$
• $y^2=72x^6+57x^5+3x^4+55x^3+14x^2+53x+38$

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 4.0.23552.1.

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_mw	$2$	(not in LMFDB)