Properties

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

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Invariants

Base field:  $\F_{79}$
Dimension:  $2$
L-polynomial:  $1 - 28 x + 349 x^{2} - 2212 x^{3} + 6241 x^{4}$
Frobenius angles:  $\pm0.133486072685$, $\pm0.269804315525$
Angle rank:  $2$ (numerical)
Number field:  4.0.232625.1
Galois group:  $D_{4}$
Jacobians:  $24$
Isomorphism classes:  24

This isogeny class is simple and geometrically 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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $4351$ $38423681$ $243446873536$ $1517631847679705$ $9468603404246763271$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $52$ $6156$ $493768$ $38963508$ $3077162772$ $243087895326$ $19203909331708$ $1517108817593508$ $119851596386235352$ $9468276089264915356$

Jacobians and polarizations

This isogeny class contains the Jacobians of 24 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 endomorphism algebra of this simple isogeny class is 4.0.232625.1.

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.bc_nl$2$(not in LMFDB)