Properties

Label 2.79.abh_qo
Base field $\F_{79}$
Dimension $2$
$p$-rank $2$
Ordinary yes
Supersingular no
Simple no
Geometrically simple no
Primitive yes
Principally polarizable yes
Contains a Jacobian no

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Invariants

Base field:  $\F_{79}$
Dimension:  $2$
L-polynomial:  $( 1 - 17 x + 79 x^{2} )( 1 - 16 x + 79 x^{2} )$
  $1 - 33 x + 430 x^{2} - 2607 x^{3} + 6241 x^{4}$
Frobenius angles:  $\pm0.0944227114288$, $\pm0.143514932644$
Angle rank:  $2$ (numerical)
Jacobians:  $0$
Isomorphism classes:  8

This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $4032$ $37545984$ $242502978816$ $1517038725242880$ $9468461809993983552$

Point counts of the (virtual) curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $47$ $6013$ $491852$ $38948281$ $3077116757$ $243088553806$ $19203921995123$ $1517108935530961$ $119851597020907748$ $9468276089931882853$

Jacobians and polarizations

This isogeny class is principally polarizable, but does not contain a Jacobian.

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{79}$.

Endomorphism algebra over $\F_{79}$
The isogeny class factors as 1.79.ar $\times$ 1.79.aq and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

TwistExtension degreeCommon base change
2.79.ab_aek$2$(not in LMFDB)
2.79.b_aek$2$(not in LMFDB)
2.79.bh_qo$2$(not in LMFDB)
2.79.am_dq$3$(not in LMFDB)
2.79.ad_aby$3$(not in LMFDB)

Below is a list of all twists of this isogeny class.

TwistExtension degreeCommon base change
2.79.ab_aek$2$(not in LMFDB)
2.79.b_aek$2$(not in LMFDB)
2.79.bh_qo$2$(not in LMFDB)
2.79.am_dq$3$(not in LMFDB)
2.79.ad_aby$3$(not in LMFDB)
2.79.abd_oc$6$(not in LMFDB)
2.79.au_io$6$(not in LMFDB)
2.79.d_aby$6$(not in LMFDB)
2.79.m_dq$6$(not in LMFDB)
2.79.u_io$6$(not in LMFDB)
2.79.bd_oc$6$(not in LMFDB)