# Properties

 Label 2.625.ado_ezc 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: $1 - 92 x + 3356 x^{2} - 57500 x^{3} + 390625 x^{4}$ Frobenius angles: $\pm0.0583496702864$, $\pm0.172477209100$ Angle rank: $2$ (numerical) Number field: 4.0.88377600.1 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 $A(\F_{q^r})$ 336390 151904977860 59598558304012710 23283042769368007601040 9094947575471190427258479750 3552713694525065016508714600065540 1387778781014084174264134650005716175910 542101086244631865119907224121059388139868160 211758236813565688774197696306079810457411633076390 82718061255302091658528916689892130663872284773070906500

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 534 388874 244115694 152587749094 95367437488974 59604645039205034 37252902990863982774 23283064365467693162494 14551915228366206118926294 9094947017729208071008668074

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
 The endomorphism algebra of this simple isogeny class is 4.0.88377600.1.
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_ezc $2$ (not in LMFDB)