Properties

Label 3.16.ar_fi_abal
Base field $\F_{2^{4}}$
Dimension $3$
$p$-rank $3$
Ordinary yes
Supersingular no
Simple yes
Geometrically simple yes
Primitive yes
Principally polarizable yes

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Invariants

Base field:  $\F_{2^{4}}$
Dimension:  $3$
L-polynomial:  $1 - 17 x + 138 x^{2} - 687 x^{3} + 2208 x^{4} - 4352 x^{5} + 4096 x^{6}$
Frobenius angles:  $\pm0.0523737408415$, $\pm0.219476755816$, $\pm0.380403485950$
Angle rank:  $3$ (numerical)
Number field:  6.0.1426375023.1
Galois group:  $S_4\times C_2$
Isomorphism classes:  12

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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $1387$ $15949113$ $69790623547$ $281625434126637$ $1151390286952763317$

Point counts of the (virtual) curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $0$ $244$ $4161$ $65572$ $1047185$ $16771987$ $268434432$ $4294969804$ $68719031508$ $1099508355239$

Jacobians and polarizations

This isogeny class is principally polarizable, but it is unknown whether it contains a Jacobian.

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{2^{4}}$.

Endomorphism algebra over $\F_{2^{4}}$
The endomorphism algebra of this simple isogeny class is 6.0.1426375023.1.

Base change

This is a primitive isogeny class.

Twists

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

TwistExtension degreeCommon base change
3.16.r_fi_bal$2$(not in LMFDB)