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

• Label: 2.211.acc_bsg
• 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: yes

Invariants

Base field:	$\F_{211}$
Dimension:	$2$
L-polynomial:	$( 1 - 28 x + 211 x^{2} )( 1 - 26 x + 211 x^{2} )$
	$1 - 54 x + 1150 x^{2} - 11394 x^{3} + 44521 x^{4}$
Frobenius angles:	$\pm0.0859092328146$, $\pm0.147206137144$
Angle rank:	$2$ (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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$34224$	$1954874880$	$88195743187056$	$3928762841804881920$	$174914239133628620533104$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$158$	$43906$	$9388586$	$1982101966$	$418227791678$	$88245958082578$	$18619893619620458$	$3928797483952937566$	$828976268014004963486$	$174913992536237129414626$

Jacobians and polarizations

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

• $y^2=111x^6+67x^5+156x^4+87x^3+195x^2+197x+108$
• $y^2=83x^6+111x^5+149x^4+209x^3+149x^2+111x+83$
• $y^2=208x^6+19x^5+32x^4+181x^3+32x^2+19x+208$
• $y^2=89x^6+170x^5+130x^4+206x^3+112x^2+69x+124$
• $y^2=186x^6+169x^5+130x^4+206x^3+130x^2+169x+186$
• $y^2=118x^6+90x^5+182x^4+18x^3+136x^2+50x+41$
• $y^2=153x^6+30x^5+78x^4+170x^3+24x^2+79x+98$
• $y^2=52x^6+138x^5+73x^4+186x^3+73x^2+138x+52$
• $y^2=78x^6+120x^5+80x^4+40x^3+80x^2+120x+78$
• $y^2=16x^6+10x^5+208x^4+3x^3+208x^2+10x+16$
• $y^2=93x^6+95x^5+35x^4+33x^3+28x^2+103x+78$
• $y^2=69x^6+100x^5+37x^4+37x^3+78x^2+134x+69$
• $y^2=58x^6+105x^5+167x^4+197x^3+89x^2+84x+144$
• $y^2=141x^6+30x^5+x^4+50x^3+21x^2+148x+133$
• $y^2=87x^6+136x^5+25x^4+146x^3+25x^2+136x+87$
• $y^2=155x^6+196x^5+179x^4+179x^3+179x^2+196x+155$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{211}$

The isogeny class factors as 1.211.abc $\times$ 1.211.aba and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.211.abc : \(\Q(\sqrt{-15}) \).
• 1.211.aba : \(\Q(\sqrt{-42}) \).

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
2.211.ac_alu	$2$	(not in LMFDB)
2.211.c_alu	$2$	(not in LMFDB)
2.211.cc_bsg	$2$	(not in LMFDB)