Properties

Label 3.16.as_ft_abcp
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:  $1 - 18 x + 149 x^{2} - 743 x^{3} + 2384 x^{4} - 4608 x^{5} + 4096 x^{6}$
Frobenius angles:  $\pm0.0886101669467$, $\pm0.128503209264$, $\pm0.379739504037$
Angle rank:  $3$ (numerical)
Number field:  6.0.6336239.1
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
$A(\F_{q^r})$ 1261 15130739 68472134809 280482881626571 1151358791893282141 4722851778072874107389 19347054850360525691260936 79234447132012101478312875371 324523361072658382358599700786221 1329229916646326550667763441789632229

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 231 4082 65303 1047154 16778940 268494316 4295307975 68720494739 1099513216676

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The endomorphism algebra of this simple isogeny class is 6.0.6336239.1.
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_ft_bcp$2$(not in LMFDB)