Abelian variety isogeny class 2.211.acg_bwp over $\F_{211}$

• Label: 2.211.acg_bwp
• Base field: $\F_{211}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: no

Invariants

Base field:	$\F_{211}$
Dimension:	$2$
L-polynomial:	$( 1 - 29 x + 211 x^{2} )^{2}$
	$1 - 58 x + 1263 x^{2} - 12238 x^{3} + 44521 x^{4}$
Frobenius angles:	$\pm0.0189887838440$, $\pm0.0189887838440$
Angle rank:	$1$ (numerical)
Jacobians:	$0$

This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.

Newton polygon

This isogeny class is ordinary.

$p$-rank:	$2$
Slopes:	$[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$33489$	$1945074609$	$88132666410000$	$3928454507855923929$	$174912958430029528857009$

Point counts of the (virtual) curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$154$	$43684$	$9381868$	$1981946404$	$418224729454$	$88245904438438$	$18619892763595354$	$3928797471347555524$	$828976267841358394708$	$174913992534024016980004$

Jacobians and polarizations

This isogeny class is principally polarizable, but does not contain a Jacobian.

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{211}$.

Endomorphism algebra over $\F_{211}$

The isogeny class factors as 1.211.abd^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
2.211.a_aqd	$2$	(not in LMFDB)
2.211.cg_bwp	$2$	(not in LMFDB)
2.211.aq_bt	$3$	(not in LMFDB)
2.211.an_abq	$3$	(not in LMFDB)
2.211.ba_wt	$3$	(not in LMFDB)
2.211.bd_yg	$3$	(not in LMFDB)
2.211.bg_bac	$3$	(not in LMFDB)