Properties

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

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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.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 19460 691452720 18731618193680 498279208845297600 13239608729463169976300 351763914326090364952439040 9346014952532839615073533084220 248314266347824112457928153937760000 6597461725641466393873125064533019681040 175287960543433453508830054567761006770343600

Point counts of the (virtual) curve

$r$ 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.
TwistExtension DegreeCommon 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.
TwistExtension DegreeCommon 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)