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

• Label: 2.29.aq_em
• Base field: $\F_{29}$
• Dimension: $2$
• $p$-rank: $1$
• Ordinary: no
• 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:	$1 - 16 x + 116 x^{2} - 464 x^{3} + 841 x^{4}$
Frobenius angles:	$\pm0.0778894863368$, $\pm0.327661210989$
Angle rank:	$2$ (numerical)
Number field:	4.0.334080.7
Galois group:	$D_{4}$
Jacobians:	$4$
Isomorphism classes:	4

This isogeny class is simple and geometrically simple, primitive, not ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

$p$-rank:	$1$
Slopes:	$[0, 1/2, 1/2, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$478$	$687364$	$596750974$	$500249771920$	$420565841187598$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$14$	$818$	$24470$	$707286$	$20504254$	$594769826$	$17249754886$	$500247472606$	$14507157992750$	$420707291300978$

Jacobians and polarizations

This isogeny class contains the Jacobians of 4 curves (of which all are hyperelliptic), and hence is principally polarizable:

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

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 4.0.334080.7.

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.q_em	$2$	(not in LMFDB)