Abelian variety isogeny class 2.53.ar_gl over $\F_{53}$

• Label: 2.53.ar_gl
• Base field: $\F_{53}$
• 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:	$\F_{53}$
Dimension:	$2$
L-polynomial:	$1 - 17 x + 167 x^{2} - 901 x^{3} + 2809 x^{4}$
Frobenius angles:	$\pm0.197207121817$, $\pm0.385018073883$
Angle rank:	$2$ (numerical)
Number field:	4.0.331525.2
Galois group:	$D_{4}$
Jacobians:	$48$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$2059$	$8019805$	$22298947351$	$62289063553525$	$174887924573492944$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$37$	$2855$	$149779$	$7894203$	$418196582$	$22164443615$	$1174713182099$	$62259701882803$	$3299763517021837$	$174887468786894150$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 48 curves (of which all are hyperelliptic):

• $y^2=28 x^6+6 x^5+9 x^4+37 x^3+26 x^2+33 x+15$
• $y^2=23 x^6+30 x^5+24 x^4+13 x^3+42 x^2+18 x+10$
• $y^2=20 x^6+20 x^5+25 x^4+36 x^3+14 x^2+10 x+30$
• $y^2=10 x^6+7 x^5+2 x^4+29 x^3+34 x^2+8 x+23$
• $y^2=7 x^6+40 x^5+41 x^4+20 x^3+39 x^2+33 x+13$
• $y^2=51 x^6+26 x^5+48 x^4+52 x^3+41 x^2+27 x$
• $y^2=51 x^6+50 x^5+34 x^4+27 x^3+4 x^2+41 x+2$
• $y^2=35 x^6+24 x^5+39 x^4+2 x^3+23 x^2+44 x+14$
• $y^2=40 x^6+33 x^5+51 x^4+17 x^3+28 x^2+17 x+36$
• $y^2=44 x^6+38 x^5+11 x^4+29 x^3+28 x^2+24 x+13$
• $y^2=49 x^6+18 x^5+19 x^4+23 x^3+27 x^2+6 x+5$
• $y^2=x^6+12 x^5+52 x^4+36 x^3+8 x^2+13 x+5$
• $y^2=21 x^6+8 x^5+24 x^4+13 x^3+6 x^2+32 x+20$
• $y^2=30 x^6+15 x^5+21 x^4+6 x^3+3 x^2+48 x+24$
• $y^2=12 x^6+33 x^5+5 x^4+23 x^3+7 x^2+52 x+26$
• $y^2=23 x^6+38 x^5+42 x^4+21 x^3+25 x^2+29 x+29$
• $y^2=35 x^6+39 x^5+18 x^3+26 x^2+31 x+30$
• $y^2=6 x^6+52 x^5+30 x^4+7 x^3+42 x^2+2 x+41$
• $y^2=29 x^6+8 x^5+43 x^4+23 x^3+39 x^2+45 x+30$
• $y^2=34 x^6+14 x^5+6 x^4+39 x^3+50 x^2+41 x+4$
• and

• $y^2=2 x^6+40 x^5+13 x^4+46 x^3+20 x^2+47 x+3$
• $y^2=49 x^6+17 x^5+51 x^4+10 x^3+47 x^2+39 x+27$
• $y^2=49 x^6+9 x^5+17 x^4+22 x^3+25 x+41$
• $y^2=2 x^6+9 x^5+24 x^4+36 x^3+25 x^2+21 x+36$
• $y^2=4 x^6+50 x^5+52 x^4+29 x^3+9 x^2+26 x+39$
• $y^2=15 x^6+40 x^5+5 x^4+9 x^3+38 x^2+36 x+30$
• $y^2=13 x^6+26 x^5+42 x^3+33 x^2+3 x+21$
• $y^2=48 x^6+47 x^5+15 x^4+41 x^3+14 x^2+40 x+41$
• $y^2=23 x^6+28 x^5+20 x^4+41 x^3+43 x^2+47 x+25$
• $y^2=22 x^6+10 x^5+40 x^3+25 x^2+20 x+43$
• $y^2=29 x^6+15 x^5+44 x^4+4 x^3+4 x^2+40 x+40$
• $y^2=51 x^6+32 x^5+4 x^4+48 x^3+7 x^2+5 x+13$
• $y^2=51 x^6+49 x^5+6 x^4+37 x^3+16 x^2+2 x+35$
• $y^2=28 x^6+51 x^5+15 x^4+51 x^3+24 x^2+13 x$
• $y^2=45 x^6+20 x^5+19 x^4+41 x^3+32 x^2+29 x+16$
• $y^2=12 x^6+3 x^5+16 x^4+22 x^3+52 x^2+30 x+22$
• $y^2=22 x^6+5 x^5+23 x^4+28 x^3+21 x^2+9 x+43$
• $y^2=19 x^6+19 x^5+46 x^4+25 x^3+26 x^2+31 x+34$
• $y^2=20 x^6+14 x^5+15 x^4+28 x^3+21 x^2+20 x+39$
• $y^2=31 x^6+10 x^5+10 x^4+16 x^3+37 x^2+32 x+24$
• $y^2=34 x^6+5 x^5+32 x^4+47 x^3+26 x^2+33 x+32$
• $y^2=24 x^6+52 x^5+7 x^4+20 x^3+12 x^2+2 x+24$
• $y^2=37 x^6+50 x^5+51 x^4+47 x^3+33 x^2+38 x+41$
• $y^2=41 x^6+35 x^5+24 x^4+x^3+2 x^2+12 x+49$
• $y^2=45 x^6+8 x^5+47 x^4+11 x^3+46 x^2+31 x+50$
• $y^2=7 x^6+34 x^5+51 x^4+44 x^3+41 x^2+46 x+3$
• $y^2=52 x^6+2 x^5+37 x^4+39 x^3+14 x^2+32 x+25$
• $y^2=2 x^6+26 x^5+11 x^4+6 x^3+37 x^2+30 x+45$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{53}$.

Endomorphism algebra over $\F_{53}$

The endomorphism algebra of this simple isogeny class is 4.0.331525.2.

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
2.53.r_gl	$2$	(not in LMFDB)