Properties

Label 2.173.abv_bii
Base Field $\F_{173}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{173}$
Dimension:  $2$
L-polynomial:  $( 1 - 26 x + 173 x^{2} )( 1 - 21 x + 173 x^{2} )$
Frobenius angles:  $\pm0.0485897903475$, $\pm0.205732831898$
Angle rank:  $2$ (numerical)
Jacobians:  21

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 21 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 22644 883116000 26796102658416 802360782054000000 24013841202718894927044 718709291817427459471104000 21510249113517197758200562606596 643780250156606239613876808024000000 19267699137141907018008637764849806997744 576662967574467440312519312529753892089900000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 127 29505 5175274 895746833 154964107307 26808754697190 4637914286350199 802359177069960193 138808137850704468562 24013807852292306846025

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The isogeny class factors as 1.173.aba $\times$ 1.173.av 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 $\F_{173}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.173.af_ahs$2$(not in LMFDB)
2.173.f_ahs$2$(not in LMFDB)
2.173.bv_bii$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.173.af_ahs$2$(not in LMFDB)
2.173.f_ahs$2$(not in LMFDB)
2.173.bv_bii$2$(not in LMFDB)
2.173.az_qo$4$(not in LMFDB)
2.173.ar_kc$4$(not in LMFDB)
2.173.r_kc$4$(not in LMFDB)
2.173.z_qo$4$(not in LMFDB)