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

• Label: 2.29.aq_el
• 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:	$1 - 16 x + 115 x^{2} - 464 x^{3} + 841 x^{4}$
Frobenius angles:	$\pm0.0484608849629$, $\pm0.334387383550$
Angle rank:	$2$ (numerical)
Number field:	4.0.182672.2
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$477$	$685449$	$595565028$	$499852030617$	$420477251811597$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$14$	$816$	$24422$	$706724$	$20499934$	$594744750$	$17249623174$	$500246663620$	$14507152072286$	$420707250641136$

Jacobians and polarizations

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

• $y^2=14x^6+15x^5+28x^4+5x^3+3x^2+25x+15$
• $y^2=27x^6+13x^5+9x^4+25x^3+x^2+11x+19$
• $y^2=10x^6+6x^5+15x^4+8x^3+21x^2+3x+18$
• $y^2=3x^6+28x^5+19x^4+9x^3+6x^2+23x+11$

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 4.0.182672.2.

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
2.29.q_el	$2$	(not in LMFDB)