# Properties

 Label 2.625.adp_fax 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: $1 - 93 x + 3403 x^{2} - 58125 x^{3} + 390625 x^{4}$ Frobenius angles: $\pm0.0431458011821$, $\pm0.164652188420$ Angle rank: $2$ (numerical) Number field: 4.0.38207421.1 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 $A(\F_{q^r})$ 335811 151869517317 59597493181061283 23283019225214002927701 9094947149560580455789122096 3552713687885537937492289054833309 1387778780919998540205212600740905673779 542101086243290233999187692782045805794918213 211758236813543244151056888538462529505175047739179 82718061255301626215128062170876309882223692158380133632

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 533 388783 244111331 152587594795 95367433022978 59604644927812255 37252902988338390767 23283064365410070544627 14551915228364663736168521 9094947017729156894965536958

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
 The endomorphism algebra of this simple isogeny class is 4.0.38207421.1.
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.dp_fax $2$ (not in LMFDB)