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

• Label: 2.17.c_bj
• Base field: $\F_{17}$
• 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:	$\F_{17}$
Dimension:	$2$
L-polynomial:	$( 1 + x + 17 x^{2} )^{2}$
	$1 + 2 x + 35 x^{2} + 34 x^{3} + 289 x^{4}$
Frobenius angles:	$\pm0.538695984895$, $\pm0.538695984895$
Angle rank:	$1$ (numerical)
Jacobians:	$3$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$361$	$104329$	$23658496$	$6890826121$	$2019863445961$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$20$	$356$	$4814$	$82500$	$1422580$	$24152222$	$410277748$	$6975569284$	$118589100398$	$2015995875236$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 3 curves (of which all are hyperelliptic):

• $y^2=9 x^6+9 x^5+2 x^4+5 x^3+5 x^2+15 x+15$
• $y^2=16 x^6+5 x^5+11 x^4+15 x^3+11 x^2+5 x+16$
• $y^2=11 x^6+6 x^3+2 x^2+4 x+3$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{17}$

The isogeny class factors as 1.17.b^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-67}) \)$)$

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
2.17.ac_bj	$2$	(not in LMFDB)
2.17.a_bh	$2$	(not in LMFDB)
2.17.ab_aq	$3$	(not in LMFDB)