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

• Label: 2.67.aw_jv
• Base field: $\F_{67}$
• 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:	$\F_{67}$
Dimension:	$2$
L-polynomial:	$( 1 - 11 x + 67 x^{2} )^{2}$
	$1 - 22 x + 255 x^{2} - 1474 x^{3} + 4489 x^{4}$
Frobenius angles:	$\pm0.265464728668$, $\pm0.265464728668$
Angle rank:	$1$ (numerical)
Jacobians:	$12$
Cyclic group of points:	no
Non-cyclic primes:	$3, 19$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$3249$	$20277009$	$90989102736$	$406422817924761$	$1822940253484324209$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$46$	$4516$	$302524$	$20168740$	$1350200986$	$90458036422$	$6060702718270$	$406067602964164$	$27206534171210308$	$1822837807073526436$

Jacobians and polarizations

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

• $y^2=12 x^6+29 x^5+45 x^4+13 x^3+42 x^2+38 x+46$
• $y^2=31 x^6+41 x^5+2 x^4+14 x^3+2 x^2+41 x+31$
• $y^2=11 x^6+13 x^5+60 x^4+6 x^3+60 x^2+13 x+11$
• $y^2=12 x^6+18 x^5+61 x^4+37 x^3+61 x^2+18 x+12$
• $y^2=27 x^6+50 x^5+58 x^4+28 x^3+31 x^2+40 x+47$
• $y^2=x^6+x^3+22$
• $y^2=38 x^6+61 x^5+63 x^4+25 x^3+55 x^2+9 x+63$
• $y^2=20 x^6+44 x^5+60 x^4+45 x^3+60 x^2+44 x+20$
• $y^2=42 x^6+51 x^5+60 x^4+19 x^3+60 x^2+51 x+42$
• $y^2=60 x^6+8 x^5+10 x^4+8 x^3+10 x^2+8 x+60$
• $y^2=44 x^6+57 x^5+58 x^4+4 x^3+27 x^2+25 x+5$
• $y^2=38 x^6+18 x^5+20 x^4+66 x^3+61 x^2+52 x+61$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{67}$

The isogeny class factors as 1.67.al^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-3}) \)$)$

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
2.67.a_n	$2$	(not in LMFDB)
2.67.w_jv	$2$	(not in LMFDB)
2.67.aq_hh	$3$	(not in LMFDB)
2.67.ak_gd	$3$	(not in LMFDB)
2.67.f_abq	$3$	(not in LMFDB)
2.67.l_cc	$3$	(not in LMFDB)
2.67.bg_pa	$3$	(not in LMFDB)