# Properties

 Label 2.625.adq_fcy 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: $1 - 94 x + 3456 x^{2} - 58750 x^{3} + 390625 x^{4}$ Frobenius angles: $\pm0.0718378155570$, $\pm0.139601802087$ Angle rank: $2$ (numerical) Number field: 4.0.8126784.1 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 $A(\F_{q^r})$ 335238 151838006388 59596773873664950 23283012271506939887568 9094947305751037807560718278 3552713697941285029025620128513300 1387778781239120804259028520524703737398 542101086251036793717738897805538910981485568 211758236813701316071394921615565104395922813606550 82718061255304423072225402427767423298134376160192534228

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 532 388702 244108384 152587549222 95367434660752 59604645096519694 37252902996904763812 23283064365742782751102 14551915228375526355820804 9094947017729464412655512302

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
 The endomorphism algebra of this simple isogeny class is 4.0.8126784.1.
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.dq_fcy $2$ (not in LMFDB)