Properties

Label 3.23.aw_io_abzl
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:  $1 - 22 x + 222 x^{2} - 1337 x^{3} + 5106 x^{4} - 11638 x^{5} + 12167 x^{6}$
Frobenius angles:  $\pm0.0586739858078$, $\pm0.151170230865$, $\pm0.361585258984$
Angle rank:  $3$ (numerical)
Number field:  6.0.1006556771.2
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
$A(\F_{q^r})$ 4499 137188007 1800065686991 21894088246506971 266486467838989230569 3243963113127485945717807 39472671948250986119517469891 480256389840624485641092893769075 5843221580966327469378901602517414208 71094346060786271174886236411051512486367

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 490 12161 279578 6432752 148027321 3404919282 78311902642 1801155908972 41426509622670

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The endomorphism algebra of this simple isogeny class is 6.0.1006556771.2.
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.w_io_bzl$2$(not in LMFDB)