Properties

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

Invariants

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

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 3825 129128175 1790119828800 21970761907111875 266887498406748676875 3244810077586313421926400 39472989695789538488552414325 480253970531619858359397768316875 5843220773624882438138013139444670400 71094382589486502645510538066686028104375

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 457 12092 280557 6442429 148065964 3404946691 78311508149 1801155660116 41426530907857

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
 The isogeny class factors as 1.23.aj 2 $\times$ 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: 1.23.aj 2 : $\mathrm{M}_{2}($$$\Q(\sqrt{-11})$$$)$ 1.23.ah : $$\Q(\sqrt{-43})$$.
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.
 Twist Extension Degree Common base change 3.23.al_y_cj $2$ (not in LMFDB) 3.23.ah_am_jl $2$ (not in LMFDB) 3.23.h_am_ajl $2$ (not in LMFDB) 3.23.l_y_acj $2$ (not in LMFDB) 3.23.z_kq_cob $2$ (not in LMFDB) 3.23.c_s_i $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.23.al_y_cj $2$ (not in LMFDB) 3.23.ah_am_jl $2$ (not in LMFDB) 3.23.h_am_ajl $2$ (not in LMFDB) 3.23.l_y_acj $2$ (not in LMFDB) 3.23.z_kq_cob $2$ (not in LMFDB) 3.23.c_s_i $3$ (not in LMFDB) 3.23.ah_cg_ajl $4$ (not in LMFDB) 3.23.h_cg_jl $4$ (not in LMFDB) 3.23.aq_fo_abfo $6$ (not in LMFDB) 3.23.ac_s_ai $6$ (not in LMFDB) 3.23.q_fo_bfo $6$ (not in LMFDB)