Properties

Label 2.97.e_cc
Base field $\F_{97}$
Dimension $2$
$p$-rank $2$
Ordinary yes
Supersingular no
Simple no
Geometrically simple no
Primitive yes
Principally polarizable yes
Contains a Jacobian yes

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Invariants

Base field:  $\F_{97}$
Dimension:  $2$
L-polynomial:  $( 1 - 10 x + 97 x^{2} )( 1 + 14 x + 97 x^{2} )$
  $1 + 4 x + 54 x^{2} + 388 x^{3} + 9409 x^{4}$
Frobenius angles:  $\pm0.330505784077$, $\pm0.751640801674$
Angle rank:  $2$ (numerical)
Jacobians:  $858$

This isogeny class is not 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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $9856$ $89413632$ $833500640896$ $7839983248441344$ $73740524911617832576$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $102$ $9502$ $913254$ $88558078$ $8587120422$ $832970238622$ $80798286784422$ $7837433494887166$ $760231061681748198$ $73742412698480887582$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 858 curves (of which all are hyperelliptic):

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{97}$.

Endomorphism algebra over $\F_{97}$
The isogeny class factors as 1.97.ak $\times$ 1.97.o and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

TwistExtension degreeCommon base change
2.97.ay_mw$2$(not in LMFDB)
2.97.ae_cc$2$(not in LMFDB)
2.97.y_mw$2$(not in LMFDB)
2.97.abd_ou$3$(not in LMFDB)
2.97.af_fo$3$(not in LMFDB)

Below is a list of all twists of this isogeny class.

TwistExtension degreeCommon base change
2.97.ay_mw$2$(not in LMFDB)
2.97.ae_cc$2$(not in LMFDB)
2.97.y_mw$2$(not in LMFDB)
2.97.abd_ou$3$(not in LMFDB)
2.97.af_fo$3$(not in LMFDB)
2.97.ap_jk$6$(not in LMFDB)
2.97.aj_e$6$(not in LMFDB)
2.97.f_fo$6$(not in LMFDB)
2.97.j_e$6$(not in LMFDB)
2.97.p_jk$6$(not in LMFDB)
2.97.bd_ou$6$(not in LMFDB)