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

• Label: 2.29.ag_ch
• 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:	$1 - 6 x + 59 x^{2} - 174 x^{3} + 841 x^{4}$
Frobenius angles:	$\pm0.317986895323$, $\pm0.494929063967$
Angle rank:	$2$ (numerical)
Number field:	4.0.608832.5
Galois group:	$D_{4}$
Jacobians:	$24$
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$721$	$779401$	$602779072$	$499839993513$	$420640696949641$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$24$	$924$	$24714$	$706708$	$20507904$	$594825126$	$17249706288$	$500245204324$	$14507151799122$	$420707308448364$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 24 curves (of which all are hyperelliptic):

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

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 4.0.608832.5.

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.g_ch	$2$	(not in LMFDB)