Properties

Label 2.625.ado_eyx
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:  $1 - 92 x + 3351 x^{2} - 57500 x^{3} + 390625 x^{4}$
Frobenius angles:  $\pm0.0226935499136$, $\pm0.181059151180$
Angle rank:  $2$ (numerical)
Number field:  4.0.33123600.1
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
$A(\F_{q^r})$ 336385 151901038065 59598221306468740 23283027173235188647785 9094947052991048445719364625 3552713680358417719217090833161360 1387778780685653008992078032040952329265 542101086237916680224343607317782193273166665 211758236813442200902980930816822681075467242885060 82718061255300018702277071747682504365333154141673036625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 534 388864 244114314 152587646884 95367432010374 59604644801528134 37252902982047725814 23283064365179278167364 14551915228357720097033034 9094947017728980147058390624

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
The endomorphism algebra of this simple isogeny class is 4.0.33123600.1.
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_eyx$2$(not in LMFDB)