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

• Label: 2.53.av_hu
• 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:	$1 - 21 x + 202 x^{2} - 1113 x^{3} + 2809 x^{4}$
Frobenius angles:	$\pm0.0631169073278$, $\pm0.347174862571$
Angle rank:	$2$ (numerical)
Number field:	4.0.90972.2
Galois group:	$D_{4}$
Jacobians:	$18$
Isomorphism classes:	18

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$1878$	$7786188$	$22182928488$	$62243783504064$	$174866561627229438$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$33$	$2773$	$149004$	$7888465$	$418145493$	$22163962714$	$1174710274449$	$62259702732865$	$3299763722378076$	$174887470774636813$

Jacobians and polarizations

This isogeny class contains the Jacobians of 18 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=30x^6+33x^5+44x^4+10x+20$
• $y^2=40x^6+50x^5+10x^4+49x^3+46x^2+17x+39$
• $y^2=20x^6+21x^5+46x^4+34x^3+18x^2+13x+38$
• $y^2=30x^6+28x^5+31x^4+35x^3+47x^2+28x+38$
• $y^2=43x^6+27x^5+x^4+29x^3+24x+5$
• $y^2=22x^6+48x^5+27x^4+x^3+10x^2+7x+30$
• $y^2=21x^6+9x^5+9x^4+51x^3+38x^2+41x+8$
• $y^2=18x^6+21x^5+38x^4+6x^3+37x^2+23x+13$
• $y^2=13x^6+52x^5+x^4+28x^3+48x^2+36x+7$
• $y^2=48x^6+43x^5+25x^4+x^3+5x^2+3x+26$
• $y^2=4x^6+30x^5+28x^4+41x^3+17x^2+36x+8$
• $y^2=20x^6+33x^5+41x^4+23x^3+32x^2+2$
• $y^2=51x^6+12x^5+16x^4+2x^3+29x^2+35x+51$
• $y^2=40x^6+35x^5+13x^4+28x^3+35x^2+31x+18$
• $y^2=3x^6+5x^5+29x^4+26x^3+11x^2+19x+40$
• $y^2=43x^6+x^5+8x^4+31x^3+29x^2+19x+45$
• $y^2=22x^6+18x^5+10x^4+6x^3+40x^2+11x+48$
• $y^2=12x^6+7x^5+44x^3+52x^2+25x+7$

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 4.0.90972.2.

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.v_hu	$2$	(not in LMFDB)