Properties

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

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Invariants

Base field:  $\F_{23}$
Dimension:  $3$
L-polynomial:  $( 1 - 9 x + 23 x^{2} )( 1 - 8 x + 23 x^{2} )( 1 - 7 x + 23 x^{2} )$
Frobenius angles:  $\pm0.112386341891$, $\pm0.186011988595$, $\pm0.239612957690$
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 does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4080 133562880 1812088131840 22041542836684800 267052133601674084400 3245030652299237537218560 39472717366089844834779768720 480250837583691795543968260300800 5843207542560698919317652488486511360 71094342156945340166822404397294527910400

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 474 12240 281458 6446400 148076028 3404923200 78310997282 1801151581680 41426507347914

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The isogeny class factors as 1.23.aj $\times$ 1.23.ai $\times$ 1.23.ah 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 are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
3.23.ak_w_bs$2$(not in LMFDB)
3.23.ai_e_fg$2$(not in LMFDB)
3.23.ag_ak_iu$2$(not in LMFDB)
3.23.g_ak_aiu$2$(not in LMFDB)
3.23.i_e_afg$2$(not in LMFDB)
3.23.k_w_abs$2$(not in LMFDB)
3.23.y_ka_cjw$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.23.ak_w_bs$2$(not in LMFDB)
3.23.ai_e_fg$2$(not in LMFDB)
3.23.ag_ak_iu$2$(not in LMFDB)
3.23.g_ak_aiu$2$(not in LMFDB)
3.23.i_e_afg$2$(not in LMFDB)
3.23.k_w_abs$2$(not in LMFDB)
3.23.y_ka_cjw$2$(not in LMFDB)