# Properties

 Label 2.11.ai_bm 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: $( 1 - 4 x + 11 x^{2} )^{2}$ Frobenius angles: $\pm0.293962833700$, $\pm0.293962833700$ Angle rank: $1$ (numerical) Jacobians: 3

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 3 curves, and hence is principally polarizable:

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

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 64 16384 1960000 220463104 25962232384 3131484160000 379411494766144 45944091111849984 5560119669688360000 672766404448046301184

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 4 134 1468 15054 161204 1767638 19469804 214332574 2358033508 25938057254

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The isogeny class factors as 1.11.ae 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-7})$$$)$
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_g $2$ 2.121.m_ks 2.11.i_bm $2$ 2.121.m_ks 2.11.e_f $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.11.a_g $2$ 2.121.m_ks 2.11.i_bm $2$ 2.121.m_ks 2.11.e_f $3$ (not in LMFDB) 2.11.a_ag $4$ (not in LMFDB) 2.11.ae_f $6$ (not in LMFDB)