Properties

Label 3.5.ah_x_acd
Base Field $\F_{5}$
Dimension $3$
$p$-rank $2$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{5}$
Dimension:  $3$
Weil polynomial:  $1 - 7 x + 23 x^{2} - 55 x^{3} + 115 x^{4} - 175 x^{5} + 125 x^{6}$
Frobenius angles:  $\pm0.0441569735346$, $\pm0.210407616474$, $\pm0.568817170463$
Angle rank:  $3$ (numerical)
Number field:  6.0.12305095.1
Galois group:  The Galois group of this isogeny class is not in the database.

This isogeny class is simple.

Newton polygon

$p$-rank:  $2$
Slopes:  $[0, 0, 1/2, 1/2, 1, 1]$

Point counts

This isogeny class does not contain a Jacobian, and it is unknown whether it is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 27 13527 1602423 232028631 31725751167 3831830854479 471824351721792 59446615346797383 7447050103389719499 930317707745221404807

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 23 101 595 3249 15695 77300 389587 1952201 9755083

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.