Properties

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

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Invariants

Base field:  $\F_{2^{4}}$
Dimension:  $3$
L-polynomial:  $( 1 - 7 x + 16 x^{2} )( 1 - 11 x + 59 x^{2} - 176 x^{3} + 256 x^{4} )$
  $1 - 18 x + 152 x^{2} - 765 x^{3} + 2432 x^{4} - 4608 x^{5} + 4096 x^{6}$
Frobenius angles:  $\pm0.133878927982$, $\pm0.160861246510$, $\pm0.347077071791$
Angle rank:  $3$ (numerical)
Isomorphism classes:  8

This isogeny class is not 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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $1290$ $15572880$ $70106706360$ $283450491672480$ $1154387250938439750$

Point counts of the (virtual) curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $-1$ $237$ $4178$ $65993$ $1049909$ $16784118$ $268490627$ $4295276561$ $68720466962$ $1099512135597$

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 $\F_{2^{4}}$.

Endomorphism algebra over $\F_{2^{4}}$
The isogeny class factors as 1.16.ah $\times$ 2.16.al_ch and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

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.ae_ac_cj$2$(not in LMFDB)
3.16.e_ac_acj$2$(not in LMFDB)
3.16.s_fw_bdl$2$(not in LMFDB)