Properties

Label 2.625.ads_fgr
Base Field $\F_{5^{4}}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{5^{4}}$
Dimension:  $2$
L-polynomial:  $( 1 - 49 x + 625 x^{2} )( 1 - 47 x + 625 x^{2} )$
Frobenius angles:  $\pm0.0637685608585$, $\pm0.110824686604$
Angle rank:  $2$ (numerical)

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 334083 151765554825 59594520668230656 23282960303572558079625 9094946329152167820319683363 3552713682724645512448755341721600 1387778781051712755653597224556698107651 542101086249637967482328403306438358193711625 211758236813711653638273301774652237911398524679168 82718061255305130044068492484991407354309930550893591625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 530 388516 244099154 152587208644 95367424420370 59604644841226846 37252902991874067314 23283064365682703621764 14551915228376236748007410 9094947017729542145031711076

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
The isogeny class factors as 1.625.abx $\times$ 1.625.abv and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{5^{4}}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.625.ac_abon$2$(not in LMFDB)
2.625.c_abon$2$(not in LMFDB)
2.625.ds_fgr$2$(not in LMFDB)