Abelian variety isogeny class 2.67.az_lb over $\F_{67}$

• Label: 2.67.az_lb
• Base field: $\F_{67}$
• 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:	$\F_{67}$
Dimension:	$2$
L-polynomial:	$1 - 25 x + 287 x^{2} - 1675 x^{3} + 4489 x^{4}$
Frobenius angles:	$\pm0.161726312859$, $\pm0.273326448036$
Angle rank:	$2$ (numerical)
Number field:	4.0.1646229.2
Galois group:	$D_{4}$
Jacobians:	$12$
Isomorphism classes:	12

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$3077$	$19929729$	$90722104919$	$406321515300861$	$1822959995386150832$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$43$	$4439$	$301639$	$20163715$	$1350215608$	$90458725043$	$6060711369049$	$406067668302739$	$27206534400816073$	$1822837805385742214$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 12 curves (of which all are hyperelliptic):

• $y^2=31 x^6+2 x^5+40 x^4+39 x^3+29 x^2+38 x+42$
• $y^2=41 x^6+35 x^5+21 x^4+55 x^3+42 x^2+53 x+51$
• $y^2=11 x^6+29 x^5+23 x^4+24 x^3+46 x^2+23 x+40$
• $y^2=3 x^6+3 x^5+65 x^4+57 x^3+63 x^2+7 x+28$
• $y^2=52 x^6+53 x^5+7 x^4+9 x^3+12 x^2+20 x+47$
• $y^2=2 x^6+13 x^5+36 x^4+17 x^3+45 x^2+11 x+24$
• $y^2=41 x^6+56 x^5+38 x^4+9 x^2+32 x+18$
• $y^2=43 x^6+30 x^5+32 x^4+40 x^3+14 x^2+17 x$
• $y^2=34 x^6+28 x^5+51 x^4+60 x^3+53 x^2+51 x+19$
• $y^2=2 x^6+55 x^5+42 x^3+3 x^2+55 x+43$
• $y^2=64 x^6+17 x^5+23 x^4+54 x^3+10 x^2+4 x+4$
• $y^2=41 x^6+50 x^5+18 x^4+48 x^3+15 x^2+58 x+50$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{67}$.

Endomorphism algebra over $\F_{67}$

The endomorphism algebra of this simple isogeny class is 4.0.1646229.2.

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
2.67.z_lb	$2$	(not in LMFDB)