Properties

Label 2.121.abn_xy
Base field $\F_{11^{2}}$
Dimension $2$
$p$-rank $2$
Ordinary yes
Supersingular no
Simple no
Geometrically simple no
Primitive yes
Principally polarizable yes
Contains a Jacobian no

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Invariants

Base field:  $\F_{11^{2}}$
Dimension:  $2$
L-polynomial:  $( 1 - 20 x + 121 x^{2} )( 1 - 19 x + 121 x^{2} )$
  $1 - 39 x + 622 x^{2} - 4719 x^{3} + 14641 x^{4}$
Frobenius angles:  $\pm0.136777651826$, $\pm0.168181340661$
Angle rank:  $2$ (numerical)
Jacobians:  $0$
Isomorphism classes:  8

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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $10506$ $210351132$ $3137188255200$ $45953897279889600$ $672761889963021866106$

Point counts of the (virtual) curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $83$ $14365$ $1770860$ $214378321$ $25937883203$ $3138434913922$ $379749905294843$ $45949730473717921$ $5559917316817969820$ $672749994925449042205$

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 $\F_{11^{2}}$.

Endomorphism algebra over $\F_{11^{2}}$
The isogeny class factors as 1.121.au $\times$ 1.121.at and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.

TwistExtension degreeCommon base change
2.121.ab_afi$2$(not in LMFDB)
2.121.b_afi$2$(not in LMFDB)
2.121.bn_xy$2$(not in LMFDB)