Properties

Label 2.121.abl_wm
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:  $( 1 - 19 x + 121 x^{2} )( 1 - 18 x + 121 x^{2} )$
  $1 - 37 x + 584 x^{2} - 4477 x^{3} + 14641 x^{4}$
Frobenius angles:  $\pm0.168181340661$, $\pm0.194982229042$
Angle rank:  $2$ (numerical)
Jacobians:  $0$
Isomorphism classes:  12

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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $10712$ $211454880$ $3139742902400$ $45957807461704320$ $672765656169997676312$

Point counts of the (virtual) curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $85$ $14441$ $1772302$ $214396561$ $25938028405$ $3138434968718$ $379749882720685$ $45949729983499681$ $5559917309905369342$ $672749994853283357801$

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.at $\times$ 1.121.as 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_adw$2$(not in LMFDB)
2.121.b_adw$2$(not in LMFDB)
2.121.bl_wm$2$(not in LMFDB)