Properties

Label 2.97.abh_rr
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:  $1 - 33 x + 459 x^{2} - 3201 x^{3} + 9409 x^{4}$
Frobenius angles:  $\pm0.0722424791852$, $\pm0.252752713219$
Angle rank:  $2$ (numerical)
Number field:  4.0.3260557.1
Galois group:  $D_{4}$
Jacobians:  $21$
Isomorphism classes:  21

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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $6635$ $86938405$ $832881418355$ $7838073177683125$ $73742816233156074800$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $65$ $9239$ $912575$ $88536507$ $8587387250$ $832971531431$ $80798271342035$ $7837433460663763$ $760231058313671885$ $73742412702024267614$

Jacobians and polarizations

This isogeny class contains the Jacobians of 21 curves (of which all are hyperelliptic), and hence is principally polarizable:

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 4.0.3260557.1.

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.bh_rr$2$(not in LMFDB)