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

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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.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 73 402157 276998281 149496636709 93676590558953 59478260049940333 37071479785304297357 23152245270339841315317 14522353952086465698392557 9095333989766520554012236597

Point counts of the (virtual) curve

$r$ 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.
TwistExtension DegreeCommon base change
4.5.l_cj_io_wh$2$(not in LMFDB)