Properties

Label 2.163.abs_bev
Base Field $\F_{163}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{163}$
Dimension:  $2$
L-polynomial:  $( 1 - 25 x + 163 x^{2} )( 1 - 19 x + 163 x^{2} )$
Frobenius angles:  $\pm0.0652307277549$, $\pm0.232879815243$
Angle rank:  $2$ (numerical)
Jacobians:  40

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 contains the Jacobians of 40 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 20155 697100985 18751177806640 498322461366498825 13239663301093020866275 351763885163745822325259520 9346014560125457979843103457035 248314265048570520303390913653335625 6597461722779315532077291816161722454320 175287960539002911616232604806683739363272425

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 120 26236 4329780 705927412 115063854600 18755369426374 3057125182221720 498311413131803428 81224760521510597580 13239635967006227806636

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The isogeny class factors as 1.163.az $\times$ 1.163.at 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.ag_aft$2$(not in LMFDB)
2.163.g_aft$2$(not in LMFDB)
2.163.bs_bev$2$(not in LMFDB)
2.163.al_gs$3$(not in LMFDB)
2.163.ac_d$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.163.ag_aft$2$(not in LMFDB)
2.163.g_aft$2$(not in LMFDB)
2.163.bs_bev$2$(not in LMFDB)
2.163.al_gs$3$(not in LMFDB)
2.163.ac_d$3$(not in LMFDB)
2.163.abk_yz$6$(not in LMFDB)
2.163.abb_sk$6$(not in LMFDB)
2.163.c_d$6$(not in LMFDB)
2.163.l_gs$6$(not in LMFDB)
2.163.bb_sk$6$(not in LMFDB)
2.163.bk_yz$6$(not in LMFDB)