Properties

Label 3.25.d_o_gx
Base field $\F_{5^{2}}$
Dimension $3$
$p$-rank $3$
Ordinary yes
Supersingular no
Simple yes
Geometrically simple yes
Primitive yes
Principally polarizable yes

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Invariants

Base field:  $\F_{5^{2}}$
Dimension:  $3$
L-polynomial:  $1 + 3 x + 14 x^{2} + 179 x^{3} + 350 x^{4} + 1875 x^{5} + 15625 x^{6}$
Frobenius angles:  $\pm0.289122521128$, $\pm0.484425495063$, $\pm0.914320774425$
Angle rank:  $3$ (numerical)
Number field:  6.0.1843390267595696.1
Galois group:  $S_4\times C_2$

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

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

Point counts

This isogeny class is principally polarizable, but it is unknown whether it contains a Jacobian.

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $18047$ $251448851$ $3923225202416$ $59495198225882795$ $931412770370049920327$

Point counts of the (virtual) curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $29$ $645$ $16064$ $389909$ $9766569$ $244150908$ $6103364121$ $152587165221$ $3814693893008$ $95367484869845$

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{2}}$
The endomorphism algebra of this simple isogeny class is 6.0.1843390267595696.1.
All geometric endomorphisms are defined over $\F_{5^{2}}$.

Base change

This is a primitive isogeny class.

Twists

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