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

• Label: 2.67.abd_nd
• 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:	$1 - 29 x + 341 x^{2} - 1943 x^{3} + 4489 x^{4}$
Frobenius angles:	$\pm0.0290076283489$, $\pm0.217444192611$
Angle rank:	$2$ (numerical)
Number field:	4.0.40053.1
Galois group:	$D_{4}$
Jacobians:	$2$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$2859$	$19449777$	$90292729293$	$406064605945869$	$1822844223778433424$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$39$	$4331$	$300213$	$20150971$	$1350129864$	$90458214743$	$6060707308191$	$406067619951139$	$27206533844397369$	$1822837800592458566$

Jacobians and polarizations

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

• $y^2=57 x^6+17 x^5+29 x^4+21 x^3+40 x^2+30 x+51$
• $y^2=48 x^6+23 x^5+12 x^4+44 x^3+13 x^2+17 x+63$

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 4.0.40053.1.

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.bd_nd	$2$	(not in LMFDB)