Properties

 Label 2.163.abt_bga Base Field $\F_{163}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian No

Invariants

 Base field: $\F_{163}$ Dimension: $2$ L-polynomial: $( 1 - 23 x + 163 x^{2} )( 1 - 22 x + 163 x^{2} )$ Frobenius angles: $\pm0.143017980409$, $\pm0.169471200781$ Angle rank: $2$ (numerical) Jacobians: 0

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

 $p$-rank: $2$ Slopes: $[0, 0, 1, 1]$

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 $A(\F_{q^r})$ 20022 696405204 18751870232424 498339725245423776 13239754048664089849482 351764196805367954013422016 9346015360336874235058179532698 248314266580324706048269890073355904 6597461724573530152385565850211217707016 175287960538074179221882105868104092499808724

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 119 26209 4329938 705951865 115064643269 18755386042498 3057125443974623 498311416205692849 81224760543600100934 13239635966936079926689

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
 The isogeny class factors as 1.163.ax $\times$ 1.163.aw 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 $\F_{163}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.163.ab_agy $2$ (not in LMFDB) 2.163.b_agy $2$ (not in LMFDB) 2.163.bt_bga $2$ (not in LMFDB)