Properties

 Label 2.11.aj_bq Base field $\F_{11}$ 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: $\F_{11}$ Dimension: $2$ L-polynomial: $( 1 - 5 x + 11 x^{2} )( 1 - 4 x + 11 x^{2} )$ Frobenius angles: $\pm0.228229222880$, $\pm0.293962833700$ Angle rank: $2$ (numerical) Jacobians: 0

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

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

Point counts

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

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 56 15232 1920800 220864000 26066804456 3136835430400 379528735785416 45941550471936000 5559792786167463200 672752920739362621312

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 3 125 1440 15081 161853 1770662 19475823 214320721 2357894880 25937537405

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The isogeny class factors as 1.11.af $\times$ 1.11.ae and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{11}$.

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 2.11.ab_c $2$ 2.121.d_iq 2.11.b_c $2$ 2.121.d_iq 2.11.j_bq $2$ 2.121.d_iq