# Properties

 Label 2.625.ads_fgp 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: $1 - 96 x + 3551 x^{2} - 60000 x^{3} + 390625 x^{4}$ Frobenius angles: $\pm0.0329685986909$, $\pm0.123763616233$ Angle rank: $2$ (numerical) Number field: 4.0.1382544.1 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 $A(\F_{q^r})$ 334081 151763978113 59594380004433604 23282953389443494065033 9094946078572247752125285601 3552713675232313439523674692790800 1387778780856318213353534037100883967361 542101086245051551821881384742752396737449993 211758236813612898211370000594869234549155590049604 82718061255303156311153815763672325272882022543262277953

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 530 388512 244098578 152587163332 95367421792850 59604644715526374 37252902986628985010 23283064365485718569092 14551915228369450326745778 9094947017729325130802729952

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
 The endomorphism algebra of this simple isogeny class is 4.0.1382544.1.
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.ds_fgp $2$ (not in LMFDB)