Properties

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

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Invariants

Base field:  $\F_{2^{4}}$
Dimension:  $3$
L-polynomial:  $( 1 - 4 x )^{2}( 1 - 11 x + 61 x^{2} - 176 x^{3} + 256 x^{4} )$
Frobenius angles:  $0$, $0$, $\pm0.189901625224$, $\pm0.315486115946$
Angle rank:  $2$ (numerical)

This isogeny class is not simple.

Newton polygon

$p$-rank:  $2$
Slopes:  $[0, 0, 1/2, 1/2, 1, 1]$

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
$A(\F_{q^r})$ 1179 14884875 69139408464 282369785083875 1152349828029027639 4719972182006527992000 19339785506519610466147299 79225780152744446567367859875 324516733024657024925157473527824 1329225292830976931805349917919921875

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 226 4123 65746 1048058 16768711 268393438 4294838146 68719091203 1099509391946

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The isogeny class factors as 1.16.ai $\times$ 2.16.al_cj and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{2^{4}}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
3.16.ad_al_fg$2$(not in LMFDB)
3.16.d_al_afg$2$(not in LMFDB)
3.16.t_gj_bgi$2$(not in LMFDB)
3.16.ah_bh_aee$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.16.ad_al_fg$2$(not in LMFDB)
3.16.d_al_afg$2$(not in LMFDB)
3.16.t_gj_bgi$2$(not in LMFDB)
3.16.ah_bh_aee$3$(not in LMFDB)
3.16.al_cz_ano$4$(not in LMFDB)
3.16.l_cz_no$4$(not in LMFDB)
3.16.ap_er_awy$6$(not in LMFDB)
3.16.h_bh_ee$6$(not in LMFDB)
3.16.p_er_wy$6$(not in LMFDB)