Properties

Label 2.53.av_ia
Base field $\F_{53}$
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:  $\F_{53}$
Dimension:  $2$
L-polynomial:  $1 - 21 x + 208 x^{2} - 1113 x^{3} + 2809 x^{4}$
Frobenius angles:  $\pm0.129472067798$, $\pm0.324486313334$
Angle rank:  $2$ (numerical)
Number field:  4.0.1389564.2
Galois group:  $D_{4}$
Jacobians:  $36$
Isomorphism classes:  36

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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $1884$ $7822368$ $22239489600$ $62288483831424$ $174888691634249004$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $33$ $2785$ $149382$ $7894129$ $418198413$ $22164295030$ $1174711787961$ $62259710775169$ $3299763802863726$ $174887471469170425$

Jacobians and polarizations

This isogeny class contains the Jacobians of 36 curves (of which all are hyperelliptic), and hence is principally polarizable:

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{53}$.

Endomorphism algebra over $\F_{53}$
The endomorphism algebra of this simple isogeny class is 4.0.1389564.2.

Base change

This is a primitive isogeny class.

Twists

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

TwistExtension degreeCommon base change
2.53.v_ia$2$(not in LMFDB)