# Properties

 Label 4.5.al_cj_aio_wh Base Field $\F_{5}$ Dimension $4$ Ordinary Yes $p$-rank $4$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{5}$ Dimension: $4$ L-polynomial: $1 - 11 x + 61 x^{2} - 222 x^{3} + 579 x^{4} - 1110 x^{5} + 1525 x^{6} - 1375 x^{7} + 625 x^{8}$ Frobenius angles: $\pm0.0374067743831$, $\pm0.206112897288$, $\pm0.309896481618$, $\pm0.465991063903$ Angle rank: $4$ (numerical) Number field: 8.0.2071948309.1 Galois group: $C_2 \wr S_4$

This isogeny class is simple and geometrically simple.

## Newton polygon

This isogeny class is ordinary.

 $p$-rank: $4$ Slopes: $[0, 0, 0, 0, 1, 1, 1, 1]$

## 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 $A(\F_{q^r})$ 73 402157 276998281 149496636709 93676590558953 59478260049940333 37071479785304297357 23152245270339841315317 14522353952086465698392557 9095333989766520554012236597

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -5 27 142 615 3070 15594 77744 388423 1949155 9766042

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
 The endomorphism algebra of this simple isogeny class is 8.0.2071948309.1.
All geometric endomorphisms are defined over $\F_{5}$.

## 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 4.5.l_cj_io_wh $2$ (not in LMFDB)