Properties

Label 3.11.ao_dq_aox
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:  $1 - 14 x + 94 x^{2} - 387 x^{3} + 1034 x^{4} - 1694 x^{5} + 1331 x^{6}$
Frobenius angles:  $\pm0.0887296077117$, $\pm0.207434636458$, $\pm0.384783505598$
Angle rank:  $3$ (numerical)
Number field:  6.0.59264075.1
Galois group:  $A_4\times C_2$

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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $365$ $1662575$ $2435836625$ $3154139198075$ $4174009280277875$

Point counts of the (virtual) curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $-2$ $114$ $1375$ $14714$ $160928$ $1772241$ $19496818$ $214391154$ $2357948500$ $25937127374$

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 6.0.59264075.1.

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.o_dq_ox$2$(not in LMFDB)