Properties

Label 2.625.adr_fes
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:  $1 - 95 x + 3502 x^{2} - 59375 x^{3} + 390625 x^{4}$
Frobenius angles:  $\pm0.0421848624330$, $\pm0.137023448831$
Angle rank:  $2$ (numerical)
Number field:  4.0.5492156.1
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
$A(\F_{q^r})$ 334658 151800199484 59595507328332704 23282979460675134555584 9094946572480227250343736258 3552713683100476302223288252173056 1387778780959752521277255835624872081074 542101086246063418946418302441254616270124800 211758236813616639899456581077861583981292031970208 82718061255303033613057664893990781518901298682645667964

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 531 388605 244103196 152587334193 95367426971851 59604644847532242 37252902989405528571 23283064365529177931169 14551915228369707453593196 9094947017729311640004387565

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
The endomorphism algebra of this simple isogeny class is 4.0.5492156.1.
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.dr_fes$2$(not in LMFDB)