Properties

Label 3.23.aw_is_acay
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:  $( 1 - 7 x + 23 x^{2} )( 1 - 15 x + 98 x^{2} - 345 x^{3} + 529 x^{4} )$
Frobenius angles:  $\pm0.0252283536038$, $\pm0.239612957690$, $\pm0.308104979730$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 4556 139541168 1821759462848 21979728282373056 266585443173655141756 3243306556454999711166464 39468526900289286522868864564 480244304486641330202298302967552 5843203369432517605014798526304526656 71094347580176791451799651413789902718768

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 498 12308 280674 6435142 147997356 3404561722 78309931970 1801150295324 41426510508018

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The isogeny class factors as 1.23.ah $\times$ 2.23.ap_du and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
Endomorphism algebra over $\overline{\F}_{23}$
The base change of $A$ to $\F_{23^{6}}$ is 1.148035889.abgac 2 $\times$ 1.148035889.hac. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{23^{6}}$.
Remainder of endomorphism lattice by field

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
3.23.ai_q_ae$2$(not in LMFDB)
3.23.i_q_e$2$(not in LMFDB)
3.23.w_is_cay$2$(not in LMFDB)
3.23.ah_ca_ahv$3$(not in LMFDB)
3.23.i_q_e$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.23.ai_q_ae$2$(not in LMFDB)
3.23.i_q_e$2$(not in LMFDB)
3.23.w_is_cay$2$(not in LMFDB)
3.23.ah_ca_ahv$3$(not in LMFDB)
3.23.i_q_e$3$(not in LMFDB)
3.23.h_ca_hv$6$(not in LMFDB)
3.23.ah_ag_hv$12$(not in LMFDB)
3.23.h_ag_ahv$12$(not in LMFDB)