# Properties

 Label 2.625.adt_fio Base Field $\F_{5^{4}}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{5^{4}}$ Dimension: $2$ L-polynomial: $( 1 - 49 x + 625 x^{2} )( 1 - 48 x + 625 x^{2} )$ Frobenius angles: $\pm0.0637685608585$, $\pm0.0903344706017$ Angle rank: $2$ (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 is principally polarizable, but does not contain a Jacobian.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 333506 151728554700 59593325970144968 23282931123531240192000 9094945732251198388598540066 3552713672138666320458752106393600 1387778780888870936100525479612747929058 542101086247553748357344467651129130339328000 211758236813693045399811901242684636196276418904776 82718061255305150026138072495087243750276259928699463500

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 529 388421 244094260 152587017409 95367418161409 59604644663623586 37252902987502815505 23283064365593187091969 14551915228374957999597364 9094947017729544342083496101

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
 The isogeny class factors as 1.625.abx $\times$ 1.625.abw and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ab_abqk $2$ (not in LMFDB) 2.625.b_abqk $2$ (not in LMFDB) 2.625.dt_fio $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.625.ab_abqk $2$ (not in LMFDB) 2.625.b_abqk $2$ (not in LMFDB) 2.625.dt_fio $2$ (not in LMFDB) 2.625.acl_cwm $4$ (not in LMFDB) 2.625.abj_vs $4$ (not in LMFDB) 2.625.bj_vs $4$ (not in LMFDB) 2.625.cl_cwm $4$ (not in LMFDB)