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

• Label: 2.67.ba_lr
• 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:	$( 1 + 13 x + 67 x^{2} )^{2}$
	$1 + 26 x + 303 x^{2} + 1742 x^{3} + 4489 x^{4}$
Frobenius angles:	$\pm0.792058120679$, $\pm0.792058120679$
Angle rank:	$1$ (numerical)
Jacobians:	$16$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$6561$	$19847025$	$90208921104$	$406380241265625$	$1822640918423900481$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$94$	$4420$	$299932$	$20166628$	$1349979274$	$90459239110$	$6060710235982$	$406067637943108$	$27206535003016804$	$1822837799318484100$

Jacobians and polarizations

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

• $y^2=34 x^6+7 x^5+7 x^4+18 x^3+7 x^2+7 x+34$
• $y^2=59 x^6+61 x^5+7 x^4+31 x^3+40 x^2+54 x+41$
• $y^2=x^6+37 x^3+1$
• $y^2=2 x^6+36 x^5+59 x^4+51 x^3+10 x^2+36 x+8$
• $y^2=62 x^6+14 x^5+3 x^4+42 x^3+3 x^2+14 x+62$
• $y^2=56 x^6+34 x^5+12 x^4+65 x^3+12 x^2+34 x+56$
• $y^2=52 x^6+39 x^5+15 x^4+30 x^3+50 x^2+57 x+11$
• $y^2=36 x^6+9 x^5+41 x^4+60 x^3+41 x^2+9 x+36$
• $y^2=37 x^6+13 x^5+8 x^4+7 x^3+8 x^2+13 x+37$
• $y^2=x^6+x^3+59$
• $y^2=33 x^6+45 x^5+13 x^4+63 x^3+13 x^2+45 x+33$
• $y^2=15 x^6+43 x^5+12 x^4+26 x^3+12 x^2+43 x+15$
• $y^2=44 x^6+12 x^5+21 x^4+19 x^3+21 x^2+12 x+44$
• $y^2=36 x^6+11 x^5+17 x^4+2 x^3+17 x^2+11 x+36$
• $y^2=x^6+x^3+24$
• $y^2=33 x^6+35 x^5+7 x^4+48 x^3+43 x^2+19 x+62$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{67}$

The isogeny class factors as 1.67.n^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-11}) \)$)$

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.aba_lr	$2$	(not in LMFDB)
2.67.a_abj	$2$	(not in LMFDB)
2.67.an_dy	$3$	(not in LMFDB)