Properties

Label 2.163.abw_bir
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:  $( 1 - 25 x + 163 x^{2} )( 1 - 23 x + 163 x^{2} )$
Frobenius angles:  $\pm0.0652307277549$, $\pm0.143017980409$
Angle rank:  $2$ (numerical)
Jacobians:  8

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 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 19599 692687457 18736672536144 498294237640546809 13239644246156138621199 351763980220145356187740416 9346015032604418486017794062247 248314266320589401909428295115928425 6597461725085037794998215278150226367056 175287960541226709478840094655054316090446177

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 116 26068 4326428 705887428 115063688996 18755374494598 3057125336771804 498311415684461956 81224760549897535844 13239635967174192988468

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The isogeny class factors as 1.163.az $\times$ 1.163.ax 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.ac_ajp$2$(not in LMFDB)
2.163.c_ajp$2$(not in LMFDB)
2.163.bw_bir$2$(not in LMFDB)
2.163.ap_fm$3$(not in LMFDB)
2.163.ag_acn$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.163.ac_ajp$2$(not in LMFDB)
2.163.c_ajp$2$(not in LMFDB)
2.163.bw_bir$2$(not in LMFDB)
2.163.ap_fm$3$(not in LMFDB)
2.163.ag_acn$3$(not in LMFDB)
2.163.abo_bbp$6$(not in LMFDB)
2.163.abf_tq$6$(not in LMFDB)
2.163.g_acn$6$(not in LMFDB)
2.163.p_fm$6$(not in LMFDB)
2.163.bf_tq$6$(not in LMFDB)
2.163.bo_bbp$6$(not in LMFDB)