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

• Label: 2.17.al_cj
• 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:	$1 - 11 x + 61 x^{2} - 187 x^{3} + 289 x^{4}$
Frobenius angles:	$\pm0.153753248596$, $\pm0.352010293509$
Angle rank:	$2$ (numerical)
Number field:	4.0.134693.2
Galois group:	$D_{4}$
Jacobians:	$5$
Isomorphism classes:	5

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$153$	$83997$	$24739641$	$7006777749$	$2016056118528$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$7$	$291$	$5035$	$83891$	$1419902$	$24137883$	$410373467$	$6976022659$	$118588717327$	$2015993387166$

Jacobians and polarizations

This isogeny class contains the Jacobians of 5 curves (of which all are hyperelliptic), and hence is principally polarizable:

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

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 4.0.134693.2.

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
2.17.l_cj	$2$	(not in LMFDB)