# Properties

 Label 2.163.abx_bjq 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: $( 1 - 25 x + 163 x^{2} )( 1 - 24 x + 163 x^{2} )$ Frobenius angles: $\pm0.0652307277549$, $\pm0.110906256499$ 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 $A(\F_{q^r})$ 19460 691452720 18731618193680 498279208845297600 13239608729463169976300 351763914326090364952439040 9346014952532839615073533084220 248314266347824112457928153937760000 6597461725641466393873125064533019681040 175287960543433453508830054567761006770343600

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 115 26021 4325260 705866137 115063380325 18755370981254 3057125310580015 498311415739115953 81224760556748015860 13239635967340870081061

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
 The isogeny class factors as 1.163.az $\times$ 1.163.ay 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 are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.163.ab_ako $2$ (not in LMFDB) 2.163.b_ako $2$ (not in LMFDB) 2.163.bx_bjq $2$ (not in LMFDB) 2.163.aq_fe $3$ (not in LMFDB) 2.163.ah_ade $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.163.ab_ako $2$ (not in LMFDB) 2.163.b_ako $2$ (not in LMFDB) 2.163.bx_bjq $2$ (not in LMFDB) 2.163.aq_fe $3$ (not in LMFDB) 2.163.ah_ade $3$ (not in LMFDB) 2.163.abp_bcg $6$ (not in LMFDB) 2.163.abg_ty $6$ (not in LMFDB) 2.163.h_ade $6$ (not in LMFDB) 2.163.q_fe $6$ (not in LMFDB) 2.163.bg_ty $6$ (not in LMFDB) 2.163.bp_bcg $6$ (not in LMFDB)