Properties

Label 2.625.ado_ezk
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:  $1 - 92 x + 3364 x^{2} - 57500 x^{3} + 390625 x^{4}$
Frobenius angles:  $\pm0.102817279181$, $\pm0.149501985083$
Angle rank:  $2$ (numerical)
Number field:  4.0.8255744.2
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
$A(\F_{q^r})$ 336398 151911281636 59599097501130446 23283067691446905676688 9094948406877052702431812718 3552713716844352505310194128418724 1387778781520906071421498361767912707182 542101086254581930780451996216848915678466048 211758236813734859340668085713610520291389144793454 82718061255304522560197978701238161149922543438717904676

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 534 388890 244117902 152587912422 95367446206894 59604645413660538 37252903004468879478 23283064365895045228542 14551915228377831431733270 9094947017729475351473779450

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
The endomorphism algebra of this simple isogeny class is 4.0.8255744.2.
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_ezk$2$(not in LMFDB)