Properties

Label 2.625.ado_eza
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:  $1 - 92 x + 3354 x^{2} - 57500 x^{3} + 390625 x^{4}$
Frobenius angles:  $\pm0.0466455273859$, $\pm0.176167524581$
Angle rank:  $2$ (numerical)
Number field:  4.0.1325376.2
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
$A(\F_{q^r})$ 336388 151903401936 59598423504934756 23283036532745666147328 9094947366742346999040908068 3552713688878452568642719268923344 1387778780883790145719730914717235385412 542101086241991763809289874310393958475972608 211758236813517943808659784039408566678090821119044 82718061255301314222275422719651299140353366898570189776

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 534 388870 244115142 152587708222 95367435300294 59604644944470598 37252902987366429078 23283064365354301674622 14551915228362925109877750 9094947017729122590988610950

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
The endomorphism algebra of this simple isogeny class is 4.0.1325376.2.
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_eza$2$(not in LMFDB)