Properties

 Label 2.173.abt_bgu Base Field $\F_{173}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian No

Invariants

 Base field: $\F_{173}$ Dimension: $2$ L-polynomial: $( 1 - 23 x + 173 x^{2} )( 1 - 22 x + 173 x^{2} )$ Frobenius angles: $\pm0.161302001611$, $\pm0.184705758688$ 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 $A(\F_{q^r})$ 22952 886222624 26811559478144 802419360182962816 24014026503592729765832 718709793140405860274661376 21510250262498122733322611579528 643780252265210088651077555367074304 19267699139601012098947827640708302935936 576662967572931989059166738770216089270286624

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 129 29609 5178258 895812225 154965303069 26808773397158 4637914534086753 802359179697965089 138808137868420325274 24013807852228366497089

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
 The isogeny class factors as 1.173.ax $\times$ 1.173.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 $\F_{173}$.

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 2.173.ab_age $2$ (not in LMFDB) 2.173.b_age $2$ (not in LMFDB) 2.173.bt_bgu $2$ (not in LMFDB)