# Properties

 Label 2.625.adq_fcz 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: $1 - 94 x + 3457 x^{2} - 58750 x^{3} + 390625 x^{4}$ Frobenius angles: $\pm0.0803816721029$, $\pm0.134758112033$ Angle rank: $2$ (numerical) Number field: 4.0.4214336.1 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 $A(\F_{q^r})$ 335239 151838794553 59596842739424284 23283015554922457794041 9094947419959294321035686119 3552713701178447176015384894145936 1387778781317956686383862021583405766551 542101086252731904893524147516277936057745833 211758236813733889960472428744809317178403170798748 82718061255304982303597754676083188528868656040454968393

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 532 388704 244108666 152587570740 95367435858312 59604645150830262 37252902999020998408 23283064365815587221732 14551915228377764816433466 9094947017729525900795164144

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
 The endomorphism algebra of this simple isogeny class is 4.0.4214336.1.
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_fcz $2$ (not in LMFDB)