# Properties

 Label 2.625.adr_fer Base Field $\F_{5^{4}}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{5^{4}}$ Dimension: $2$ L-polynomial: $1 - 95 x + 3501 x^{2} - 59375 x^{3} + 390625 x^{4}$ Frobenius angles: $\pm0.0290941168115$, $\pm0.140487243861$ Angle rank: $2$ (numerical) Number field: 4.0.4189941.1 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 $A(\F_{q^r})$ 334657 151799411229 59595437729566537 23282976089367302716725 9094946452572333143055185152 3552713679596209585298569610152029 1387778780870773896157574925328902004417 542101086244037128726421977909571765750847525 211758236813574433532409168615400859615299001431897 82718061255302219063435103437595335470496162038459797504

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 531 388603 244102911 152587312099 95367425714526 59604644788740403 37252902987017026791 23283064365442149428899 14551915228366807054134771 9094947017729222079326246878

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
 The endomorphism algebra of this simple isogeny class is 4.0.4189941.1.
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.dr_fer $2$ (not in LMFDB)