# Properties

 Label 2.625.adq_fdb 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: $( 1 - 47 x + 625 x^{2} )^{2}$ Frobenius angles: $\pm0.110824686604$, $\pm0.110824686604$ Angle rank: $1$ (numerical)

This isogeny class is not 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 $A(\F_{q^r})$ 335241 151840370889 59596980471005184 23283022119922727318025 9094947648106872037487293161 3552713707631750105700258712387584 1387778781474462885533364750853735186569 542101086256070718392927977768083565271913225 211758236813797122090637960350980070950981764448256 82718061255306038246267171712633858082363146845274097929

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 532 388708 244109230 152587613764 95367438250612 59604645259098718 37252903003222179700 23283064365958988169604 14551915228382110095331342 9094947017729642002919493028

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
 The isogeny class factors as 1.625.abv 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-291})$$$)$
All geometric endomorphisms are defined over $\F_{5^{4}}$.

## Base change

This is a primitive isogeny class.

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.625.a_abkx $2$ (not in LMFDB) 2.625.dq_fdb $2$ (not in LMFDB) 2.625.bv_ciy $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.625.a_abkx $2$ (not in LMFDB) 2.625.dq_fdb $2$ (not in LMFDB) 2.625.bv_ciy $3$ (not in LMFDB) 2.625.a_bkx $4$ (not in LMFDB) 2.625.abv_ciy $6$ (not in LMFDB)