Properties

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

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Invariants

Base field:  $\F_{2^{4}}$
Dimension:  $3$
L-polynomial:  $1 - 19 x + 166 x^{2} - 847 x^{3} + 2656 x^{4} - 4864 x^{5} + 4096 x^{6}$
Frobenius angles:  $\pm0.0709775673297$, $\pm0.201826864759$, $\pm0.297497433083$
Angle rank:  $3$ (numerical)
Number field:  6.0.6989311.1
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
$A(\F_{q^r})$ 1189 15039661 69763800961 283728032496181 1154270968031109109 4721852659308591068899 19341146348278687484428456 79226931708935740855514213461 324518833910587692334706450612029 1329229544618382160146437891616435211

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 228 4159 66060 1049803 16775391 268412324 4294900572 68719536082 1099512908943

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The endomorphism algebra of this simple isogeny class is 6.0.6989311.1.
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.t_gk_bgp$2$(not in LMFDB)