Properties

Label 2.79.abe_os
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 yes

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Invariants

Base field:  $\F_{79}$
Dimension:  $2$
L-polynomial:  $( 1 - 16 x + 79 x^{2} )( 1 - 14 x + 79 x^{2} )$
  $1 - 30 x + 382 x^{2} - 2370 x^{3} + 6241 x^{4}$
Frobenius angles:  $\pm0.143514932644$, $\pm0.211343260462$
Angle rank:  $2$ (numerical)
Jacobians:  $16$
Isomorphism classes:  64

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

Newton polygon

This isogeny class is ordinary.

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

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $4224$ $38117376$ $243221387904$ $1517650948915200$ $9468827658790667904$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $50$ $6106$ $493310$ $38963998$ $3077235650$ $243089005786$ $19203918316430$ $1517108835586558$ $119851595744281490$ $9468276078104526106$

Jacobians and polarizations

This isogeny class contains the Jacobians of 16 curves (of which all are hyperelliptic), and hence is principally polarizable:

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{79}$
The isogeny class factors as 1.79.aq $\times$ 1.79.ao 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 is a list of all twists of this isogeny class.

TwistExtension degreeCommon base change
2.79.ac_aco$2$(not in LMFDB)
2.79.c_aco$2$(not in LMFDB)
2.79.be_os$2$(not in LMFDB)