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

• Label: 2.29.aq_eq
• 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:	$1 - 16 x + 120 x^{2} - 464 x^{3} + 841 x^{4}$
Frobenius angles:	$\pm0.161460008254$, $\pm0.290576523077$
Angle rank:	$2$ (numerical)
Number field:	4.0.127232.1
Galois group:	$D_{4}$
Jacobians:	$4$
Isomorphism classes:	4

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$482$	$695044$	$601501778$	$501813427472$	$420887454213922$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$14$	$826$	$24662$	$709494$	$20519934$	$594838090$	$17249856134$	$500246533470$	$14507149790126$	$420707258085786$

Jacobians and polarizations

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

• $y^2=12x^6+16x^5+22x^4+26x^3+5x^2+9x+18$
• $y^2=10x^6+8x^5+x^4+15x^3+21x^2+3x+17$
• $y^2=11x^6+15x^5+5x^4+17x^3+x^2+6x+2$
• $y^2=18x^5+6x^4+27x^3+9x^2+10x+2$

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 4.0.127232.1.

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.q_eq	$2$	(not in LMFDB)