# Properties

 Label 2.11.ag_bf 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: $( 1 - 3 x + 11 x^{2} )^{2}$ Frobenius angles: $\pm0.350615407277$, $\pm0.350615407277$ Angle rank: $1$ (numerical) Jacobians: 5

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 5 curves, and hence is principally polarizable:

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

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 81 18225 1971216 216531225 25753509441 3129502521600 379700649556281 45959999942637225 5560321723022501136 672749671959787640625

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 6 148 1476 14788 159906 1766518 19484646 214406788 2358119196 25937412148

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The isogeny class factors as 1.11.ad 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-35})$$$)$
All geometric endomorphisms are defined over $\F_{11}$.

## Base change

This is a primitive isogeny class.

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.11.a_n $2$ 2.121.ba_pv 2.11.g_bf $2$ 2.121.ba_pv 2.11.d_ac $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.11.a_n $2$ 2.121.ba_pv 2.11.g_bf $2$ 2.121.ba_pv 2.11.d_ac $3$ (not in LMFDB) 2.11.a_an $4$ (not in LMFDB) 2.11.ad_ac $6$ (not in LMFDB)