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

• Label: 2.17.al_ch
• 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:	$1 - 11 x + 59 x^{2} - 187 x^{3} + 289 x^{4}$
Frobenius angles:	$\pm0.106224360187$, $\pm0.372781387459$
Angle rank:	$2$ (numerical)
Number field:	4.0.185661.1
Galois group:	$D_{4}$
Jacobians:	$2$
Isomorphism classes:	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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$151$	$82597$	$24407791$	$6965983189$	$2013247390576$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$7$	$287$	$4969$	$83403$	$1417922$	$24134447$	$410380397$	$6976073011$	$118588861603$	$2015994822782$

Jacobians and polarizations

This isogeny class contains the Jacobians of 2 curves (of which all are hyperelliptic), and hence is principally polarizable:

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

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 4.0.185661.1.

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.l_ch	$2$	(not in LMFDB)