Properties

Label 2.625.ado_ezh
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:  $1 - 92 x + 3361 x^{2} - 57500 x^{3} + 390625 x^{4}$
Frobenius angles:  $\pm0.0848020128811$, $\pm0.160677945551$
Angle rank:  $2$ (numerical)
Number field:  4.0.2533025.1
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
$A(\F_{q^r})$ 336395 151908917705 59598895302060080 23283058350244280188745 9094948095757887734947054875 3552713708524700111747800167614720 1387778781333536756637379397094815395355 542101086250964829445032574087166264362023305 211758236813675490133754727081694320139854753087920 82718061255303737135558090120234366669712312758437847625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 534 388884 244117074 152587851204 95367442944574 59604645274079934 37252902999439222734 23283064365739691909124 14551915228373751610899954 9094947017729388993121349524

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
The endomorphism algebra of this simple isogeny class is 4.0.2533025.1.
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_ezh$2$(not in LMFDB)