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

• Label: 2.53.f_eh
• 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:	$1 + 5 x + 111 x^{2} + 265 x^{3} + 2809 x^{4}$
Frobenius angles:	$\pm0.530257552113$, $\pm0.579933521437$
Angle rank:	$2$ (numerical)
Number field:	4.0.1044725.2
Galois group:	$D_{4}$
Jacobians:	$16$
Isomorphism classes:	16
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$3191$	$8459341$	$22053859379$	$62194775359541$	$174911559990097936$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$59$	$3007$	$148133$	$7882251$	$418253094$	$22164630823$	$1174707671693$	$62259685673043$	$3299763767190779$	$174887470176014022$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 16 curves (of which all are hyperelliptic):

• $y^2=25 x^6+17 x^5+3 x^4+44 x^3+42 x^2+28 x+25$
• $y^2=14 x^6+32 x^5+41 x^4+44 x^3+22 x^2+40 x+52$
• $y^2=37 x^6+29 x^5+50 x^4+48 x^3+3 x^2+49 x+39$
• $y^2=39 x^6+51 x^5+30 x^4+16 x^3+38 x^2+14 x+27$
• $y^2=27 x^6+49 x^5+21 x^4+40 x^3+17 x^2+48 x+22$
• $y^2=44 x^6+2 x^5+10 x^4+47 x^3+5 x^2+38 x+39$
• $y^2=19 x^6+13 x^5+28 x^4+3 x^3+20 x^2+6 x+47$
• $y^2=49 x^6+24 x^5+17 x^4+35 x^3+31 x^2+25 x+24$
• $y^2=8 x^6+5 x^5+11 x^4+9 x^3+44 x^2+35 x+27$
• $y^2=2 x^6+45 x^5+28 x^4+39 x^3+28 x^2+38 x+22$
• $y^2=10 x^6+21 x^5+23 x^4+49 x^3+7 x^2+28 x+22$
• $y^2=51 x^6+12 x^5+19 x^4+8 x^3+30 x^2+24 x+19$
• $y^2=18 x^6+31 x^5+46 x^4+11 x^3+40 x^2+12 x+16$
• $y^2=12 x^6+8 x^5+6 x^4+43 x^3+29 x^2+24 x+26$
• $y^2=48 x^6+49 x^5+48 x^4+47 x^3+9 x^2+47 x+20$
• $y^2=35 x^6+12 x^5+5 x^4+6 x^3+49 x^2+42 x+11$

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 4.0.1044725.2.

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.af_eh	$2$	(not in LMFDB)