Properties

Label 2.83.abd_om
Base field $\F_{83}$
Dimension $2$
$p$-rank $2$
Ordinary yes
Supersingular no
Simple no
Geometrically simple no
Primitive yes
Principally polarizable yes
Contains a Jacobian no

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Invariants

Base field:  $\F_{83}$
Dimension:  $2$
L-polynomial:  $( 1 - 15 x + 83 x^{2} )( 1 - 14 x + 83 x^{2} )$
  $1 - 29 x + 376 x^{2} - 2407 x^{3} + 6889 x^{4}$
Frobenius angles:  $\pm0.192168636682$, $\pm0.221078141621$
Angle rank:  $2$ (numerical)
Jacobians:  $0$
Isomorphism classes:  12

This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $4830$ $46860660$ $327571894440$ $2253392306272800$ $15516999503618647650$

Point counts of the (virtual) curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $55$ $6801$ $572890$ $47481497$ $3939283925$ $326941980354$ $27136054309055$ $2252292150101233$ $186940253832387070$ $15516041173351970961$

Jacobians and polarizations

This isogeny class is principally polarizable, but does not contain a Jacobian.

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{83}$.

Endomorphism algebra over $\F_{83}$
The isogeny class factors as 1.83.ap $\times$ 1.83.ao 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 is a list of all twists of this isogeny class.

TwistExtension degreeCommon base change
2.83.ab_abs$2$(not in LMFDB)
2.83.b_abs$2$(not in LMFDB)
2.83.bd_om$2$(not in LMFDB)