Properties

Label 2.113.abk_vd
Base field $\F_{113}$
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:  $\F_{113}$
Dimension:  $2$
L-polynomial:  $( 1 - 19 x + 113 x^{2} )( 1 - 17 x + 113 x^{2} )$
  $1 - 36 x + 549 x^{2} - 4068 x^{3} + 12769 x^{4}$
Frobenius angles:  $\pm0.148111132014$, $\pm0.205038125192$
Angle rank:  $2$ (numerical)
Jacobians:  $6$
Isomorphism classes:  8

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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $9215$ $160552945$ $2082577615040$ $26589151546802425$ $339465155397052785575$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $78$ $12572$ $1443330$ $163076244$ $18424808598$ $2081956626974$ $235260584712294$ $26584442062552036$ $3004041936655364130$ $339456738958019549132$

Jacobians and polarizations

This isogeny class contains the Jacobians of 6 curves (of which all are hyperelliptic), and hence is principally polarizable:

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{113}$.

Endomorphism algebra over $\F_{113}$
The isogeny class factors as 1.113.at $\times$ 1.113.ar 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
2.113.ac_adt$2$(not in LMFDB)
2.113.c_adt$2$(not in LMFDB)
2.113.bk_vd$2$(not in LMFDB)