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

• Label: 2.53.q_fw
• 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:	$1 + 16 x + 152 x^{2} + 848 x^{3} + 2809 x^{4}$
Frobenius angles:	$\pm0.583082070841$, $\pm0.817931441478$
Angle rank:	$2$ (numerical)
Number field:	4.0.786688.1
Galois group:	$D_{4}$
Jacobians:	$36$
Cyclic group of points:	yes

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$3826$	$8026948$	$22067055682$	$62266544702224$	$174887543253853426$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$70$	$2858$	$148222$	$7891350$	$418195670$	$22164647834$	$1174707632462$	$62259700362910$	$3299763722079142$	$174887468937348938$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 36 curves (of which all are hyperelliptic):

• $y^2=51 x^6+40 x^5+20 x^4+35 x^3+5 x^2+6 x+42$
• $y^2=7 x^6+38 x^5+34 x^4+18 x^3+31 x^2+43 x+23$
• $y^2=9 x^6+4 x^5+7 x^4+18 x^3+25 x^2+37 x+35$
• $y^2=x^6+45 x^5+24 x^4+24 x^3+28 x^2+25 x+38$
• $y^2=24 x^6+48 x^5+28 x^4+46 x^3+44 x^2+2 x+30$
• $y^2=41 x^6+39 x^5+8 x^4+27 x^3+41 x^2+23 x+16$
• $y^2=13 x^6+28 x^5+9 x^4+45 x^3+2 x^2+38 x+29$
• $y^2=29 x^6+26 x^5+x^4+31 x^3+46 x^2+2 x+25$
• $y^2=33 x^6+34 x^5+43 x^4+35 x^3+50 x^2+30 x+34$
• $y^2=22 x^6+4 x^5+37 x^4+13 x^3+5 x^2+37 x+28$
• $y^2=38 x^6+17 x^5+30 x^4+19 x^3+52 x^2+17 x+28$
• $y^2=7 x^6+14 x^5+25 x^4+35 x^3+4 x^2+10 x+44$
• $y^2=20 x^6+11 x^5+8 x^4+48 x^2+25 x+37$
• $y^2=19 x^6+52 x^4+21 x^3+23 x^2+34 x+20$
• $y^2=15 x^5+34 x^4+39 x^3+27 x^2+9 x+15$
• $y^2=43 x^6+17 x^5+15 x^4+12 x^3+5 x^2+44 x+24$
• $y^2=11 x^6+12 x^5+5 x^4+26 x^3+36 x^2+21 x+11$
• $y^2=7 x^6+19 x^5+22 x^4+45 x^3+25 x^2+6 x+41$
• $y^2=44 x^6+44 x^5+37 x^4+7 x^3+52 x^2+34 x+30$
• $y^2=41 x^6+36 x^5+9 x^4+9 x^3+47 x^2+28 x$
• and

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

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 4.0.786688.1.

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
2.53.aq_fw	$2$	(not in LMFDB)