Properties

Label 2.97.bc_om
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:  $1 + 28 x + 376 x^{2} + 2716 x^{3} + 9409 x^{4}$
Frobenius angles:  $\pm0.674361963755$, $\pm0.856942942614$
Angle rank:  $2$ (numerical)
Number field:  4.0.64940288.1
Galois group:  $D_{4}$
Jacobians:  $56$
Isomorphism classes:  56

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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $12530$ $88236260$ $831618618530$ $7838776984010000$ $73742040248119207650$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $126$ $9378$ $911190$ $88544454$ $8587296886$ $832971846306$ $80798277983262$ $7837433810920446$ $760231055872321950$ $73742412705107798818$

Jacobians and polarizations

This isogeny class contains the Jacobians of 56 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 4.0.64940288.1.

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.abc_om$2$(not in LMFDB)