Properties

Label 2.97.ac_bq
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:  $1 - 2 x + 42 x^{2} - 194 x^{3} + 9409 x^{4}$
Frobenius angles:  $\pm0.262533165452$, $\pm0.695850649419$
Angle rank:  $2$ (numerical)
Number field:  4.0.3911904.1
Galois group:  $D_{4}$
Jacobians:  $896$
Cyclic group of points:    no
Non-cyclic primes:   $2$

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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $9256$ $89301888$ $832662586600$ $7840374277791744$ $73743399891370856296$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $96$ $9490$ $912336$ $88562494$ $8587455216$ $832970021650$ $80798285306688$ $7837433389142014$ $760231056742899072$ $73742412713110786450$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 896 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 4.0.3911904.1.

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.c_bq$2$(not in LMFDB)