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

• Label: 2.29.h_ce
• 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:	$1 + 7 x + 56 x^{2} + 203 x^{3} + 841 x^{4}$
Frobenius angles:	$\pm0.491874122996$, $\pm0.736054514509$
Angle rank:	$2$ (numerical)
Number field:	4.0.1484793.1
Galois group:	$D_{4}$
Jacobians:	$20$
Isomorphism classes:	20
Cyclic group of points:	no
Non-cyclic primes:	$2$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$1108$	$762304$	$589402816$	$500233032448$	$420583946381188$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$37$	$905$	$24166$	$707265$	$20505137$	$594858854$	$17250156149$	$500243699233$	$14507147144926$	$420707290395905$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 20 curves (of which all are hyperelliptic):

• $y^2=22 x^6+4 x^5+5 x^4+x^3+15 x^2+23 x+1$
• $y^2=22 x^6+16 x^5+27 x^4+25 x^3+28 x^2+10 x+4$
• $y^2=23 x^6+11 x^5+18 x^4+25 x^3+19 x^2+3 x+24$
• $y^2=8 x^6+9 x^5+28 x^4+25 x^3+17 x^2+3 x+3$
• $y^2=28 x^6+26 x^5+x^4+23 x^3+9 x^2+17 x+11$
• $y^2=24 x^6+8 x^5+10 x^4+11 x^3+15 x^2+21 x+20$
• $y^2=17 x^6+22 x^5+17 x^4+2 x^3+19 x^2+2 x+9$
• $y^2=15 x^6+12 x^5+9 x^4+25 x^3+21 x^2+7 x+28$
• $y^2=3 x^6+5 x^5+20 x^4+13 x^3+6 x^2+19 x+15$
• $y^2=6 x^6+6 x^5+23 x^4+13 x^3+25 x^2+16 x+3$
• $y^2=23 x^6+20 x^5+17 x^3+4 x^2+13 x+6$
• $y^2=14 x^6+3 x^5+11 x^3+6 x^2+3 x+14$
• $y^2=20 x^6+26 x^5+26 x^2+8 x+16$
• $y^2=19 x^6+4 x^5+24 x^4+12 x^3+18 x^2+27 x+18$
• $y^2=19 x^6+24 x^5+3 x^4+12 x^3+4 x^2+11 x+9$
• $y^2=9 x^6+4 x^5+x^4+4 x^3+9 x^2+9 x+16$
• $y^2=15 x^6+27 x^5+19 x^4+5 x^3+17 x^2+24 x+3$
• $y^2=3 x^6+20 x^5+26 x^4+6 x^3+13 x^2+18 x+1$
• $y^2=24 x^5+7 x^4+x^3+28 x^2+27 x+22$
• $y^2=2 x^6+26 x^5+26 x^4+4 x^3+15 x+27$

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 4.0.1484793.1.

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.ah_ce	$2$	(not in LMFDB)