# Properties

 Label 2.625.adp_fbg 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: $( 1 - 47 x + 625 x^{2} )( 1 - 46 x + 625 x^{2} )$ Frobenius angles: $\pm0.110824686604$, $\pm0.128188433698$ 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 $A(\F_{q^r})$ 335820 151876609920 59598106375173120 23283048017878968614400 9094948130978993416376009100 3552713714994581251298615244226560 1387778781559245817396443727360110749580 542101086256494093614950235812542126769305600 211758236813784433138617642436074387903758455034880 82718061255305500689141663355134714590349180341217225600

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 533 388801 244113842 152587783489 95367443313893 59604645382626526 37252903005498054197 23283064365977171996929 14551915228381238117188178 9094947017729582897888484001

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
 The isogeny class factors as 1.625.abv $\times$ 1.625.abu 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 is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.625.ab_abjc $2$ (not in LMFDB) 2.625.b_abjc $2$ (not in LMFDB) 2.625.dp_fbg $2$ (not in LMFDB)