Properties

Label 3.16.ar_fh_abad
Base Field $\F_{2^{4}}$
Dimension $3$
Ordinary Yes
$p$-rank $3$
Principally polarizable Yes

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Invariants

Base field:  $\F_{2^{4}}$
Dimension:  $3$
L-polynomial:  $1 - 17 x + 137 x^{2} - 679 x^{3} + 2192 x^{4} - 4352 x^{5} + 4096 x^{6}$
Frobenius angles:  $\pm0.0557975217823$, $\pm0.199707648000$, $\pm0.392692232151$
Angle rank:  $3$ (numerical)
Number field:  6.0.1519449968.1
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 it is unknown whether it contains a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 1378 15811172 69340848382 281086272464400 1151494351752562038 4722088902457997803772 19344425151281449548869098 79229209671482692551852470400 324516313945408408736325045072778 1329223451034376432587487392646392132

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 242 4134 65446 1047280 16776230 268457826 4295024062 68719002456 1099507868442

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The endomorphism algebra of this simple isogeny class is 6.0.1519449968.1.
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.r_fh_bad$2$(not in LMFDB)