Abelian variety isogeny class 2.29.k_cx over $\F_{29}$

• Label: 2.29.k_cx
• Base field: $\F_{29}$
• 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:	$\F_{29}$
Dimension:	$2$
L-polynomial:	$1 + 10 x + 75 x^{2} + 290 x^{3} + 841 x^{4}$
Frobenius angles:	$\pm0.564622382094$, $\pm0.759017030091$
Angle rank:	$2$ (numerical)
Number field:	4.0.389696.1
Galois group:	$D_{4}$
Jacobians:	$21$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$1217$	$750889$	$585639872$	$500609436521$	$420716448591577$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$40$	$892$	$24010$	$707796$	$20511600$	$594848422$	$17249762080$	$500245109988$	$14507159915410$	$420707203645452$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 21 curves (of which all are hyperelliptic):

• $y^2=6 x^6+25 x^5+5 x^4+17 x^3+16 x^2+23 x+21$
• $y^2=22 x^6+17 x^4+10 x^2+11 x+4$
• $y^2=12 x^6+27 x^5+19 x^4+2 x^3+7 x^2+24 x+16$
• $y^2=18 x^6+23 x^5+6 x^4+18 x^3+26 x^2+16 x+1$
• $y^2=16 x^6+11 x^5+27 x^4+11 x^3+4 x^2+14 x+10$
• $y^2=x^6+9 x^5+13 x^4+13 x^2+20 x+25$
• $y^2=14 x^6+24 x^5+5 x^4+10 x^3+7 x^2+7 x+11$
• $y^2=22 x^6+13 x^5+23 x^4+2 x^3+8 x^2+7 x+13$
• $y^2=16 x^6+14 x^5+26 x^4+8 x^3+9 x^2+12 x+6$
• $y^2=17 x^6+28 x^5+x^4+18 x^3+13 x^2+13 x+25$
• $y^2=20 x^6+14 x^5+25 x^4+6 x^3+28 x^2+9 x+15$
• $y^2=17 x^6+18 x^5+24 x^4+23 x^3+12 x^2+15 x+23$
• $y^2=3 x^6+8 x^5+3 x^4+8 x^3+6 x+10$
• $y^2=7 x^6+10 x^5+28 x^4+5 x^3+12 x^2+28 x+21$
• $y^2=16 x^6+20 x^5+24 x^4+27 x^3+28 x^2+7 x+16$
• $y^2=16 x^6+16 x^5+10 x^4+26 x^3+7 x^2+28 x+22$
• $y^2=20 x^6+x^5+7 x^4+21 x^3+3 x^2+11 x+17$
• $y^2=5 x^6+11 x^5+12 x^4+10 x^3+22 x^2+9 x+7$
• $y^2=14 x^6+19 x^5+25 x^4+15 x^3+4 x^2+2 x+24$
• $y^2=x^6+15 x^5+7 x^4+12 x^3+26 x^2+x+7$
• $y^2=6 x^6+13 x^5+17 x^4+5 x^3+26 x^2+25 x+1$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{29}$.

Endomorphism algebra over $\F_{29}$

The endomorphism algebra of this simple isogeny class is 4.0.389696.1.

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
2.29.ak_cx	$2$	(not in LMFDB)