Properties

Label 2.17.am_cq
Base Field $\F_{17}$
Dimension $2$
$p$-rank $1$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{17}$
Dimension:  $2$
Weil polynomial:  $1 - 12 x + 68 x^{2} - 204 x^{3} + 289 x^{4}$
Frobenius angles:  $\pm0.144218155731$, $\pm0.312293972145$
Angle rank:  $2$ (numerical)
Number field:  4.0.39168.3
Galois group:  $D_4$

This isogeny class is simple.

Newton polygon

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

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 142 81508 24674062 7021751184 2017512450862 582619693995556 168380578563662446 48662217800185909248 14063200526825718750958 4064237743953971910957988

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 282 5022 84070 1420926 24137466 410345382 6975904510 118588855302 2015997043962

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.