# Properties

 Label 2.625.ado_ezd Base Field $\F_{5^{4}}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

# Learn more about

## Invariants

 Base field: $\F_{5^{4}}$ Dimension: $2$ L-polynomial: $( 1 - 49 x + 625 x^{2} )( 1 - 43 x + 625 x^{2} )$ Frobenius angles: $\pm0.0637685608585$, $\pm0.170463428383$ 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 contains a Jacobian, and hence is principally polarizable.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 336391 151905765825 59598625703581888 23283045886763785505625 9094947679704005460682452991 3552713697338350150689668151705600 1387778781078692401589796220056514049263 542101086245928974960116970885078365534475625 211758236813588739509881050636883247271221964865216 82718061255302454695965997198025275049032278585159616625

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 534 388876 244115970 152587769524 95367438581934 59604645086404126 37252902992598296670 23283064365523403605924 14551915228367790153420834 9094947017729247987397006876

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
 The isogeny class factors as 1.625.abx $\times$ 1.625.abr 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.ag_abgz $2$ (not in LMFDB) 2.625.g_abgz $2$ (not in LMFDB) 2.625.do_ezd $2$ (not in LMFDB)