Properties

Label 2.97.ae_fu
Base field $\F_{97}$
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:  $\F_{97}$
Dimension:  $2$
L-polynomial:  $1 - 4 x + 150 x^{2} - 388 x^{3} + 9409 x^{4}$
Frobenius angles:  $\pm0.350260612824$, $\pm0.580493617304$
Angle rank:  $2$ (numerical)
Number field:  4.0.1009152.1
Galois group:  $D_{4}$
Jacobians:  $624$

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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $9168$ $91239936$ $833493400272$ $7837059412156416$ $73742800109858585808$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $94$ $9694$ $913246$ $88525054$ $8587385374$ $832970369374$ $80798264146078$ $7837433815668478$ $760231061530444510$ $73742412675302732254$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 624 curves (of which all are hyperelliptic):

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{97}$.

Endomorphism algebra over $\F_{97}$
The endomorphism algebra of this simple isogeny class is 4.0.1009152.1.

Base change

This is a primitive isogeny class.

Twists

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

TwistExtension degreeCommon base change
2.97.e_fu$2$(not in LMFDB)