Properties

Label 3.23.aw_im_abys
Base Field $\F_{23}$
Dimension $3$
Ordinary Yes
$p$-rank $3$
Principally polarizable Yes

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Invariants

Base field:  $\F_{23}$
Dimension:  $3$
L-polynomial:  $( 1 - 9 x + 23 x^{2} )( 1 - 13 x + 80 x^{2} - 299 x^{3} + 529 x^{4} )$
Frobenius angles:  $\pm0.0682102518540$, $\pm0.112386341891$, $\pm0.376537722378$
Angle rank:  $3$ (numerical)

This isogeny class is not 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
$A(\F_{q^r})$ 4470 136004220 1788990337440 21845982486952800 266379289777152535350 3243912648770318047902720 39473108555003491979848812810 480257945969618293622382624393600 5843225776768365182277811583496048480 71094364834113573421699535163954054191100

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 486 12086 278962 6430162 148025016 3404956942 78312156386 1801157202314 41426520561846

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The isogeny class factors as 1.23.aj $\times$ 2.23.an_dc 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 $\F_{23}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.23.ae_ao_es$2$(not in LMFDB)
3.23.e_ao_aes$2$(not in LMFDB)
3.23.w_im_bys$2$(not in LMFDB)