Properties

Label 2.97.am_hq
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:  $1 - 12 x + 198 x^{2} - 1164 x^{3} + 9409 x^{4}$
Frobenius angles:  $\pm0.298422611217$, $\pm0.494454574715$
Angle rank:  $2$ (numerical)
Number field:  4.0.391168.1
Galois group:  $D_{4}$
Jacobians:  $468$

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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $8432$ $90930688$ $834715392752$ $7837138502017024$ $73742313677385616112$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $86$ $9662$ $914582$ $88525950$ $8587328726$ $832972376126$ $80798269384982$ $7837433357690110$ $760231059343339862$ $73742412723561129662$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 468 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 4.0.391168.1.

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.m_hq$2$(not in LMFDB)