Properties

Label 2.625.ado_ezj
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:  $1 - 92 x + 3363 x^{2} - 57500 x^{3} + 390625 x^{4}$
Frobenius angles:  $\pm0.0962392443412$, $\pm0.153912608943$
Angle rank:  $2$ (numerical)
Number field:  4.0.17246736.2
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
$A(\F_{q^r})$ 336397 151910493657 59599030101420148 23283064578322958497881 9094948303258402163513750917 3552713714077810760486326122149904 1387778781458807816841256984511310301717 542101086253391418061574036348813205112835433 211758236813715609642293250194646288882360525305524 82718061255304277424701314962594398935886188654410858057

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 534 388888 244117626 152587892020 95367445120374 59604645367245670 37252903002801942150 23283064365843913096612 14551915228376508602533626 9094947017729448398540883208

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
The endomorphism algebra of this simple isogeny class is 4.0.17246736.2.
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_ezj$2$(not in LMFDB)