Abelian variety isogeny class 2.17.c_p over $\F_{17}$

• Label: 2.17.c_p
• Base field: $\F_{17}$
• 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:	$\F_{17}$
Dimension:	$2$
L-polynomial:	$1 + 2 x + 15 x^{2} + 34 x^{3} + 289 x^{4}$
Frobenius angles:	$\pm0.361658764124$, $\pm0.730969710122$
Angle rank:	$2$ (numerical)
Number field:	4.0.53225.1
Galois group:	$D_{4}$
Jacobians:	$20$
Isomorphism classes:	20
Cyclic group of points:	yes

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$341$	$91729$	$24230096$	$7030936121$	$2011628605261$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$20$	$316$	$4934$	$84180$	$1416780$	$24125662$	$410380508$	$6975766884$	$118588524518$	$2015994481836$

Jacobians and polarizations

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

• $y^2=11 x^6+15 x^5+13 x^4+16 x^3+6 x^2+7 x+16$
• $y^2=9 x^6+x^5+16 x^4+5 x^2+16 x+7$
• $y^2=5 x^6+2 x^5+11 x^4+5 x^3+8 x^2+14 x+8$
• $y^2=15 x^6+10 x^5+16 x^4+15 x^3+15 x^2+5 x+13$
• $y^2=14 x^6+4 x^5+x^4+16 x^2+14 x+6$
• $y^2=13 x^6+8 x^5+5 x^4+5 x^3+5 x^2+13 x+15$
• $y^2=6 x^6+15 x^5+x^4+10 x^3+3 x^2+15 x+16$
• $y^2=2 x^6+4 x^5+2 x^4+13 x^3+4 x^2+3 x+8$
• $y^2=x^6+8 x^5+5 x^4+6 x^2+10 x+16$
• $y^2=13 x^6+5 x^5+5 x^4+14 x^3+13 x^2+15 x+5$
• $y^2=16 x^6+4 x^5+7 x^4+7 x^3+10 x^2+7 x+16$
• $y^2=x^6+2 x^5+9 x^4+5 x^3+3 x^2+9 x+7$
• $y^2=x^6+11 x^5+15 x^4+7 x^3+11 x^2+14 x+7$
• $y^2=15 x^6+11 x^5+x^4+16 x^3+x^2+15 x+7$
• $y^2=16 x^6+13 x^5+12 x^4+2 x^3+12 x^2+16 x+4$
• $y^2=9 x^6+3 x^5+12 x^4+5 x^3+8 x^2+11 x+13$
• $y^2=6 x^6+13 x^5+4 x^4+15 x^3+13 x^2+9 x+16$
• $y^2=16 x^6+12 x^5+5 x^4+9 x^3+2 x^2+x+1$
• $y^2=13 x^6+3 x^5+5 x^4+4 x^3+10 x^2+9 x+12$
• $y^2=x^6+x^5+14 x^4+16 x^3+4 x^2+7 x+12$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{17}$.

Endomorphism algebra over $\F_{17}$

The endomorphism algebra of this simple isogeny class is 4.0.53225.1.

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
2.17.ac_p	$2$	(not in LMFDB)