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

• Label: 2.29.an_dg
• 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:	$1 - 13 x + 84 x^{2} - 377 x^{3} + 841 x^{4}$
Frobenius angles:	$\pm0.0672107836573$, $\pm0.426379556366$
Angle rank:	$2$ (numerical)
Number field:	4.0.591500.2
Galois group:	$D_{4}$
Jacobians:	$12$
Isomorphism classes:	24

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$536$	$705376$	$593553536$	$498743154560$	$420445732619896$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$17$	$841$	$24338$	$705153$	$20498397$	$594817606$	$17250114353$	$500246970273$	$14507141795642$	$420707226692481$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 12 curves (of which all are hyperelliptic):

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

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 4.0.591500.2.

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.n_dg	$2$	(not in LMFDB)