Properties

Label 3.23.ax_ji_acfa
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:  $( 1 - 8 x + 23 x^{2} )( 1 - 15 x + 99 x^{2} - 345 x^{3} + 529 x^{4} )$
Frobenius angles:  $\pm0.0783210629050$, $\pm0.186011988595$, $\pm0.297557123995$
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
$A(\F_{q^r})$ 4304 136212992 1813789084688 21994887726770176 266778314171123801344 3244182270233356521972224 39471269160916924675667467024 480250962505635770440652925542400 5843216362374378008408379484224743696 71094367988087099265650410260656908009472

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 485 12253 280865 6439796 148037321 3404798279 78311017649 1801154300359 41426522399660

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The isogeny class factors as 1.23.ai $\times$ 2.23.ap_dv 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.ah_c_dy$2$(not in LMFDB)
3.23.h_c_ady$2$(not in LMFDB)
3.23.x_ji_cfa$2$(not in LMFDB)