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

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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:

Point counts of the abelian variety

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

Point counts of the curve

$r$ 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.
TwistExtension DegreeCommon 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.
TwistExtension DegreeCommon 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)