Properties

Label 3.16.as_fr_abca
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:  $( 1 - 4 x )^{2}( 1 - 10 x + 51 x^{2} - 160 x^{3} + 256 x^{4} )$
Frobenius angles:  $0$, $0$, $\pm0.118775077357$, $\pm0.396715540983$
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
$A(\F_{q^r})$ 1242 14841900 67410885150 278530575717600 1149080543839229562 4720642471404865687500 19344294699311758106125422 79230199569895617471844502400 324517952317539894662554871999850 1329225045583212868416758049548947500

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 227 4019 64847 1045079 16771091 268456019 4295077727 68719349399 1099509187427

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
The isogeny class factors as 1.16.ai $\times$ 2.16.ak_bz 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.ac_an_dk$2$(not in LMFDB)
3.16.c_an_adk$2$(not in LMFDB)
3.16.s_fr_bca$2$(not in LMFDB)
3.16.ag_bb_aem$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.16.ac_an_dk$2$(not in LMFDB)
3.16.c_an_adk$2$(not in LMFDB)
3.16.s_fr_bca$2$(not in LMFDB)
3.16.ag_bb_aem$3$(not in LMFDB)
3.16.ak_cp_ami$4$(not in LMFDB)
3.16.k_cp_mi$4$(not in LMFDB)
3.16.ao_ed_aue$6$(not in LMFDB)
3.16.g_bb_em$6$(not in LMFDB)
3.16.o_ed_ue$6$(not in LMFDB)