Properties

Label 2.625.ado_eyy
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:  $1 - 92 x + 3352 x^{2} - 57500 x^{3} + 390625 x^{4}$
Frobenius angles:  $\pm0.0323716859977$, $\pm0.179501015972$
Angle rank:  $2$ (numerical)
Number field:  4.0.57714944.1
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
$A(\F_{q^r})$ 336386 151901826020 59598288705937298 23283030293682276630800 9094947157662552418964888466 3552713683205112446386194305772260 1387778780752058392349732672612450530178 542101086239290385863148871578522095147827200 211758236813468000086067126038063183318733958001346 82718061255300467876616583714006604835189433125970544100

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 534 388866 244114590 152587667334 95367433107934 59604644849287746 37252902983830281750 23283064365238278375294 14551915228359493003394934 9094947017729029534299309826

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
The endomorphism algebra of this simple isogeny class is 4.0.57714944.1.
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.do_eyy$2$(not in LMFDB)