Properties

 Label 1.163.az Base Field $\F_{163}$ Dimension $1$ Ordinary Yes $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

Invariants

 Base field: $\F_{163}$ Dimension: $1$ L-polynomial: $1 - 25 x + 163 x^{2}$ Frobenius angles: $\pm0.0652307277549$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-3})$$ Galois group: $C_2$ Jacobians: 2

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class contains the Jacobians of 2 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 139 26271 4327348 705875499 115063264669 18755366679504 3057125226189943 498311414414939475 81224760538723362124 13239635967124119157311

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 139 26271 4327348 705875499 115063264669 18755366679504 3057125226189943 498311414414939475 81224760538723362124 13239635967124119157311

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-3})$$.
All geometric endomorphisms are defined over $\F_{163}$.

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 1.163.z $2$ (not in LMFDB) 1.163.i $3$ (not in LMFDB) 1.163.r $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 1.163.z $2$ (not in LMFDB) 1.163.i $3$ (not in LMFDB) 1.163.r $3$ (not in LMFDB) 1.163.ar $6$ (not in LMFDB) 1.163.ai $6$ (not in LMFDB)