Properties

Label 3.23.ax_jh_aceq
Base Field $\F_{23}$
Dimension $3$
Ordinary No
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{23}$
Dimension:  $3$
L-polynomial:  $( 1 - 9 x + 23 x^{2} )( 1 - 14 x + 92 x^{2} - 322 x^{3} + 529 x^{4} )$
Frobenius angles:  $\pm0.112386341891$, $\pm0.135789939707$, $\pm0.314924263207$
Angle rank:  $3$ (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
$A(\F_{q^r})$ 4290 135624060 1808039324520 21969744191881200 266739205154465707950 3244372546491988002336960 39472897837403617193938415370 480257541194117605634752487193600 5843233974769971834562226813683119960 71094398476475424486958657923029006922300

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 483 12214 280543 6438851 148046004 3404938769 78312090383 1801159729318 41426540165163

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The isogeny class factors as 1.23.aj $\times$ 2.23.ao_do 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.af_al_hc$2$(not in LMFDB)
3.23.f_al_ahc$2$(not in LMFDB)
3.23.x_jh_ceq$2$(not in LMFDB)