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

• Label: 2.29.aq_ep
• 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:	$1 - 16 x + 119 x^{2} - 464 x^{3} + 841 x^{4}$
Frobenius angles:	$\pm0.140915858920$, $\pm0.302284266018$
Angle rank:	$2$ (numerical)
Number field:	4.0.235152.2
Galois group:	$D_{4}$
Jacobians:	$4$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$481$	$693121$	$600313012$	$501426604393$	$420811961468041$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$14$	$824$	$24614$	$708948$	$20516254$	$594825806$	$17249893318$	$500247356644$	$14507155910942$	$420707285765864$

Jacobians and polarizations

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

• $y^2=15 x^6+12 x^5+28 x^4+19 x^3+11 x^2+27 x+23$
• $y^2=19 x^6+6 x^5+28 x^4+3 x^3+15 x^2+20 x+3$
• $y^2=19 x^6+22 x^5+21 x^4+3 x^3+18 x^2+21 x+15$
• $y^2=8 x^6+3 x^5+3 x^4+19 x^3+6 x^2+3 x+26$

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 4.0.235152.2.

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_ep	$2$	(not in LMFDB)