Properties

Label 3.16.as_fw_abdn
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:  $1 - 18 x + 152 x^{2} - 767 x^{3} + 2432 x^{4} - 4608 x^{5} + 4096 x^{6}$
Frobenius angles:  $\pm0.0594651251591$, $\pm0.214320821692$, $\pm0.338587853715$
Angle rank:  $3$ (numerical)
Number field:  6.0.140908967.1
Galois group:  $S_4\times C_2$

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
$A(\F_{q^r})$ 1288 15551312 69975592288 282817808471072 1152494692905722488 4720505980388038652672 19341260518734792235936408 79227943246712797108920262208 324518861037962270499397503970912 1329227345214895437215676396980068112

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 237 4172 65849 1048189 16770606 268413907 4294955409 68719541828 1099511089637

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The endomorphism algebra of this simple isogeny class is 6.0.140908967.1.
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_fw_bdn$2$(not in LMFDB)