Properties

Label 3.11.an_cy_alf
Base field $\F_{11}$
Dimension $3$
$p$-rank $3$
Ordinary yes
Supersingular no
Simple yes
Geometrically simple yes
Primitive yes
Principally polarizable yes
Contains a Jacobian no

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Invariants

Base field:  $\F_{11}$
Dimension:  $3$
L-polynomial:  $1 - 13 x + 76 x^{2} - 291 x^{3} + 836 x^{4} - 1573 x^{5} + 1331 x^{6}$
Frobenius angles:  $\pm0.0354721676546$, $\pm0.103262097857$, $\pm0.494210615205$
Angle rank:  $3$ (numerical)
Number field:  6.0.2343728.1
Galois group:  $S_4\times C_2$

This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $367$ $1512407$ $2178396028$ $3027725383475$ $4158835374916837$

Point counts of the (virtual) curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $-1$ $105$ $1226$ $14117$ $160339$ $1773096$ $19487705$ $214336533$ $2357974370$ $25937919845$

Jacobians and polarizations

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

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{11}$.

Endomorphism algebra over $\F_{11}$
The endomorphism algebra of this simple isogeny class is 6.0.2343728.1.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.

TwistExtension degreeCommon base change
3.11.n_cy_lf$2$(not in LMFDB)