Properties

Label 2.97.i_hu
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:  $1 + 8 x + 202 x^{2} + 776 x^{3} + 9409 x^{4}$
Frobenius angles:  $\pm0.518943488750$, $\pm0.612684523000$
Angle rank:  $2$ (numerical)
Number field:  4.0.527936.1
Galois group:  $D_{4}$
Jacobians:  $220$
Isomorphism classes:  280

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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $10396$ $91775888$ $831141747100$ $7835558066054144$ $73744439397538819996$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $106$ $9750$ $910666$ $88508094$ $8587576266$ $832972755990$ $80798266131178$ $7837433605654014$ $760231059467008042$ $73742412687885817750$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 220 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 4.0.527936.1.

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.ai_hu$2$(not in LMFDB)