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

• Label: 2.29.am_dq
• Base field: $\F_{29}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{29}$
Dimension:	$2$
L-polynomial:	$( 1 - 6 x + 29 x^{2} )^{2}$
	$1 - 12 x + 94 x^{2} - 348 x^{3} + 841 x^{4}$
Frobenius angles:	$\pm0.311919362152$, $\pm0.311919362152$
Angle rank:	$1$ (numerical)
Jacobians:	$26$
Cyclic group of points:	no
Non-cyclic primes:	$2, 3$

This isogeny class is not 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$576$	$746496$	$609892416$	$501943910400$	$420638113567296$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$18$	$886$	$25002$	$709678$	$20507778$	$594733606$	$17249435802$	$500246371678$	$14507158502898$	$420707309659606$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 26 curves (of which all are hyperelliptic):

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

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{29}$.

Endomorphism algebra over $\F_{29}$

The isogeny class factors as 1.29.ag^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-5}) \)$)$

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

Twist	Extension degree	Common base change
2.29.a_w	$2$	(not in LMFDB)
2.29.m_dq	$2$	(not in LMFDB)
2.29.g_h	$3$	(not in LMFDB)