# 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

## 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.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 336388 151903401936 59598423504934756 23283036532745666147328 9094947366742346999040908068 3552713688878452568642719268923344 1387778780883790145719730914717235385412 542101086241991763809289874310393958475972608 211758236813517943808659784039408566678090821119044 82718061255301314222275422719651299140353366898570189776

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