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

• Label: 2.67.az_kt
• 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:	$1 - 25 x + 279 x^{2} - 1675 x^{3} + 4489 x^{4}$
Frobenius angles:	$\pm0.0801786736356$, $\pm0.311310056841$
Angle rank:	$2$ (numerical)
Number field:	4.0.76725.1
Galois group:	$D_{4}$
Jacobians:	$16$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$3069$	$19853361$	$90540836991$	$406100916175581$	$1822789878103055664$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$43$	$4423$	$301039$	$20152771$	$1350089608$	$90457795987$	$6060708382849$	$406067693674963$	$27206534875826473$	$1822837809276767878$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 16 curves (of which all are hyperelliptic):

• $y^2=45 x^6+17 x^5+60 x^4+52 x^3+39 x^2+40 x+64$
• $y^2=43 x^6+4 x^5+38 x^4+61 x^3+27 x^2+12 x+43$
• $y^2=28 x^6+62 x^5+53 x^4+17 x^3+21 x^2+57 x+42$
• $y^2=52 x^6+14 x^5+51 x^4+18 x^3+39 x^2+56 x+29$
• $y^2=27 x^6+30 x^5+19 x^4+58 x^3+52 x^2+x+18$
• $y^2=46 x^6+4 x^5+46 x^4+49 x^3+52 x^2+8 x+57$
• $y^2=20 x^6+48 x^5+52 x^4+33 x^3+27 x^2+44 x+54$
• $y^2=46 x^6+22 x^5+25 x^4+66 x^3+33 x^2+22 x+22$
• $y^2=42 x^6+30 x^5+38 x^4+10 x^3+5 x^2+5 x+61$
• $y^2=52 x^6+56 x^5+65 x^4+61 x^3+46 x^2+12 x+33$
• $y^2=30 x^6+31 x^5+35 x^4+21 x^3+54 x^2+16 x+18$
• $y^2=49 x^6+46 x^5+35 x^4+6 x^3+6 x^2+27 x+50$
• $y^2=53 x^6+40 x^5+52 x^4+8 x^3+36 x^2+52 x+7$
• $y^2=2 x^6+10 x^5+41 x^4+62 x^3+30 x^2+27 x+38$
• $y^2=8 x^6+60 x^5+64 x^4+48 x^3+17 x^2+53 x+50$
• $y^2=31 x^6+12 x^5+49 x^4+41 x^3+35 x+16$

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 4.0.76725.1.

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
2.67.z_kt	$2$	(not in LMFDB)