Properties

Label 2.97.e_abq
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

Related objects

Downloads

Learn more

Invariants

Base field:  $\F_{97}$
Dimension:  $2$
L-polynomial:  $1 + 4 x - 42 x^{2} + 388 x^{3} + 9409 x^{4}$
Frobenius angles:  $\pm0.259824402676$, $\pm0.847918240528$
Angle rank:  $2$ (numerical)
Number field:  4.0.3801600.1
Galois group:  $D_{4}$
Jacobians:  $780$
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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $9760$ $87605760$ $834554966560$ $7839643225497600$ $73742190142365844000$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $102$ $9310$ $914406$ $88554238$ $8587314342$ $832973425630$ $80798251727526$ $7837433560293118$ $760231057107987942$ $73742412693587475550$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 780 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 4.0.3801600.1.

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.ae_abq$2$(not in LMFDB)