# Properties

 Label 2.11.ah_bg 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 Yes

## Invariants

 Base field: $\F_{11}$ Dimension: $2$ L-polynomial: $( 1 - 5 x + 11 x^{2} )( 1 - 2 x + 11 x^{2} )$ Frobenius angles: $\pm0.228229222880$, $\pm0.402508885479$ Angle rank: $2$ (numerical) Jacobians: 4

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 contains the Jacobians of 4 curves, and hence is principally polarizable:

• $y^2=4x^5+x^4+9x^3+5x^2+9x+2$
• $y^2=7x^6+5x^5+10x^4+8x^3+5x^2+2$
• $y^2=6x^6+6x^5+2x^4+x^3+8x^2+9x+7$
• $y^2=4x^6+10x^5+3x^4+6x^3+8x^2+9x+10$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 70 16660 1907080 216580000 25924764250 3139068936640 379842475317130 45949204763280000 5559605596299406120 672736387628404676500

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 5 137 1430 14793 160975 1771922 19491925 214356433 2357815490 25936899977

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The isogeny class factors as 1.11.af $\times$ 1.11.ac 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.ad_m $2$ 2.121.p_hg 2.11.d_m $2$ 2.121.p_hg 2.11.h_bg $2$ 2.121.p_hg