Properties

Label 2.625.adq_fcu
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:  $1 - 94 x + 3452 x^{2} - 58750 x^{3} + 390625 x^{4}$
Frobenius angles:  $\pm0.0379132483954$, $\pm0.152726660511$
Angle rank:  $2$ (numerical)
Number field:  4.0.14742336.1
Galois group:  $D_{4}$

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 a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 335234 151834853748 59596498410834914 23282999131742312029776 9094946848021560706084093394 3552713684922548537397791324172756 1387778780919888627021561399559220144786 542101086244084615462953756858782048304043008 211758236813564607006974347534594991213309986416818 82718061255301976083697732020726539790032277720423925268

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 532 388694 244107256 152587463110 95367429861112 59604644878101542 37252902988335440308 23283064365444188968702 14551915228366131780448756 9094947017729195363421591494

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
The endomorphism algebra of this simple isogeny class is 4.0.14742336.1.
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.dq_fcu$2$(not in LMFDB)