Properties

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

Learn more about

Invariants

Base field:  $\F_{23}$
Dimension:  $3$
L-polynomial:  $( 1 - 8 x + 23 x^{2} )( 1 - 15 x + 98 x^{2} - 345 x^{3} + 529 x^{4} )$
Frobenius angles:  $\pm0.0252283536038$, $\pm0.186011988595$, $\pm0.308104979730$
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
$A(\F_{q^r})$ 4288 135569408 1806958037248 21955079523926016 266619757351864728128 3243700904414625914814464 39470030019402046689305152448 480247748814072984699441493573632 5843206516583315293893099586494221056 71094334669235078925275532301062062317568

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 483 12208 280359 6435971 148015356 3404691389 78310493615 1801151265424 41426502984843

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The isogeny class factors as 1.23.ai $\times$ 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.bhqk. 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.ah_b_dq$2$(not in LMFDB)
3.23.h_b_adq$2$(not in LMFDB)
3.23.x_jh_ces$2$(not in LMFDB)
3.23.ai_ca_aiy$3$(not in LMFDB)
3.23.h_b_adq$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.23.ah_b_dq$2$(not in LMFDB)
3.23.h_b_adq$2$(not in LMFDB)
3.23.x_jh_ces$2$(not in LMFDB)
3.23.ai_ca_aiy$3$(not in LMFDB)
3.23.h_b_adq$3$(not in LMFDB)
3.23.ai_ca_aiy$6$(not in LMFDB)
3.23.ah_b_dq$6$(not in LMFDB)
3.23.i_ca_iy$6$(not in LMFDB)
3.23.ai_ag_iy$12$(not in LMFDB)
3.23.i_ag_aiy$12$(not in LMFDB)