# Properties

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

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## Invariants

 Base field: $\F_{5^{4}}$ Dimension: $2$ L-polynomial: $1 - 94 x + 3454 x^{2} - 58750 x^{3} + 390625 x^{4}$ Frobenius angles: $\pm0.0557136983427$, $\pm0.146976429221$ Angle rank: $2$ (numerical) Number field: 4.0.940400.1 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 $A(\F_{q^r})$ 335236 151836430064 59596636142208484 23283005702845137370880 9094947077065589467415204836 3552713691445935794461443973380464 1387778781080282739536857440222428501764 542101086247595083078705287136302963691089920 211758236813634246642815022051958454081011265338756 82718061255303241733195532825154572337319874560784353904

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 532 388698 244107820 152587506174 95367432262812 59604644987545818 37252902992640986980 23283064365594962404734 14551915228370917379783812 9094947017729334523055543578

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
 The endomorphism algebra of this simple isogeny class is 4.0.940400.1.
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_fcw $2$ (not in LMFDB)