Properties

Label 2.131.g_b
Base field $\F_{131}$
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:  $\F_{131}$
Dimension:  $2$
L-polynomial:  $1 + 6 x + x^{2} + 786 x^{3} + 17161 x^{4}$
Frobenius angles:  $\pm0.300401032106$, $\pm0.822720592890$
Angle rank:  $2$ (numerical)
Number field:  4.0.724392000.1
Galois group:  $D_{4}$
Jacobians:  576

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class contains the Jacobians of 576 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $17955$ $293941305$ $5059662908580$ $86744524991098905$ $1488362726025477421875$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $138$ $17128$ $2250648$ $294548548$ $38579119098$ $5053913893438$ $662062535692878$ $86730203442289348$ $11361656660456567448$ $1488377021750445489448$

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{131}$
The endomorphism algebra of this simple isogeny class is 4.0.724392000.1.
All geometric endomorphisms are defined over $\F_{131}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension degreeCommon base change
2.131.ag_b$2$(not in LMFDB)