Properties

Label 3.16.as_fx_abdv
Base Field $\F_{2^{4}}$
Dimension $3$
Ordinary Yes
$p$-rank $3$
Principally polarizable Yes
Contains a Jacobian No

Learn more about

Invariants

Base field:  $\F_{2^{4}}$
Dimension:  $3$
L-polynomial:  $1 - 18 x + 153 x^{2} - 775 x^{3} + 2448 x^{4} - 4608 x^{5} + 4096 x^{6}$
Frobenius angles:  $\pm0.0553436146881$, $\pm0.250233467979$, $\pm0.311381340818$
Angle rank:  $3$ (numerical)
Number field:  6.0.17734383.1
Galois group:  $A_4\times C_2$

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

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

Point counts

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

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 1297 15692403 70479380773 283564876383003 1152655576178040397 4719085573232509917957 19338322668810231270834568 79225244273442154807936680267 324518813798067695711289364535917 1329230812957638618341794282862547693

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 239 4202 66023 1048334 16765556 268373132 4294809095 68719531823 1099513958084

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The endomorphism algebra of this simple isogeny class is 6.0.17734383.1.
All geometric endomorphisms are defined over $\F_{2^{4}}$.

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.s_fx_bdv$2$(not in LMFDB)