Properties

Label 2.625.ado_eyz
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:  $1 - 92 x + 3353 x^{2} - 57500 x^{3} + 390625 x^{4}$
Frobenius angles:  $\pm0.0400093343905$, $\pm0.177873335421$
Angle rank:  $2$ (numerical)
Number field:  4.0.4665921.1
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
$A(\F_{q^r})$ 336387 151902613977 59598356105425968 23283033413519102437161 9094947262246318603237424067 3552713686045123824442152274608384 1387778780818104056610542627104743218787 542101086240648742000863111413101593351397833 211758236813493247349501871654776710279896062964144 82718061255300899695208571847146296575064435869964222457

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 534 388868 244114866 152587687780 95367434204574 59604644896935230 37252902985603181550 23283064365296619327172 14551915228361227982127186 9094947017729077013255607908

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
The endomorphism algebra of this simple isogeny class is 4.0.4665921.1.
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_eyz$2$(not in LMFDB)