Properties

Label 3.8.al_cf_ahj
Base field $\F_{2^{3}}$
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:  $\F_{2^{3}}$
Dimension:  $3$
L-polynomial:  $( 1 - 5 x + 8 x^{2} )( 1 - 6 x + 19 x^{2} - 48 x^{3} + 64 x^{4} )$
  $1 - 11 x + 57 x^{2} - 191 x^{3} + 456 x^{4} - 704 x^{5} + 512 x^{6}$
Frobenius angles:  $\pm0.0864530894824$, $\pm0.154919815756$, $\pm0.468973809368$
Angle rank:  $3$ (numerical)
Isomorphism classes:  24

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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $120$ $231840$ $128793240$ $66565900800$ $35216945352600$

Point counts of the (virtual) curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $-2$ $58$ $490$ $3966$ $32798$ $264058$ $2102714$ $16782014$ $134225230$ $1073828218$

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 $\F_{2^{3}}$.

Endomorphism algebra over $\F_{2^{3}}$
The isogeny class factors as 1.8.af $\times$ 2.8.ag_t 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
3.8.ab_ad_ab$2$(not in LMFDB)
3.8.b_ad_b$2$(not in LMFDB)
3.8.l_cf_hj$2$(not in LMFDB)