# 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

# Learn more about

## 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.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 336395 151908917705 59598895302060080 23283058350244280188745 9094948095757887734947054875 3552713708524700111747800167614720 1387778781333536756637379397094815395355 542101086250964829445032574087166264362023305 211758236813675490133754727081694320139854753087920 82718061255303737135558090120234366669712312758437847625

 $r$ 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.
 Twist Extension Degree Common base change 2.625.do_ezh $2$ (not in LMFDB)