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

• Label: 2.67.w_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:	$\pm0.734535271332$, $\pm0.734535271332$
Angle rank:	$1$ (numerical)
Jacobians:	$12$
Cyclic group of points:	no
Non-cyclic primes:	$79$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$6241$	$20277009$	$89930413456$	$406422817924761$	$1822735363898434561$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$90$	$4516$	$299004$	$20168740$	$1350049230$	$90458036422$	$6060720492378$	$406067602964164$	$27206534621379588$	$1822837807073526436$

Jacobians and polarizations

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

• $y^2=6 x^6+48 x^5+56 x^4+40 x^3+21 x^2+19 x+23$
• $y^2=49 x^6+54 x^5+x^4+7 x^3+x^2+54 x+49$
• $y^2=22 x^6+26 x^5+53 x^4+12 x^3+53 x^2+26 x+22$
• $y^2=6 x^6+9 x^5+64 x^4+52 x^3+64 x^2+9 x+6$
• $y^2=54 x^6+33 x^5+49 x^4+56 x^3+62 x^2+13 x+27$
• $y^2=2 x^6+2 x^3+44$
• $y^2=9 x^6+55 x^5+59 x^4+50 x^3+43 x^2+18 x+59$
• $y^2=40 x^6+21 x^5+53 x^4+23 x^3+53 x^2+21 x+40$
• $y^2=21 x^6+59 x^5+30 x^4+43 x^3+30 x^2+59 x+21$
• $y^2=30 x^6+4 x^5+5 x^4+4 x^3+5 x^2+4 x+30$
• $y^2=22 x^6+62 x^5+29 x^4+2 x^3+47 x^2+46 x+36$
• $y^2=19 x^6+9 x^5+10 x^4+33 x^3+64 x^2+26 x+64$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{67}$

The isogeny class factors as 1.67.l^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.aw_jv	$2$	(not in LMFDB)
2.67.a_n	$2$	(not in LMFDB)
2.67.abg_pa	$3$	(not in LMFDB)
2.67.al_cc	$3$	(not in LMFDB)
2.67.af_abq	$3$	(not in LMFDB)
2.67.k_gd	$3$	(not in LMFDB)
2.67.q_hh	$3$	(not in LMFDB)