Properties

Label 2.7.ad_c
Base Field $\F_{7}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{7}$
Dimension:  $2$
Weil polynomial:  $1 - 3 x + 2 x^{2} - 21 x^{3} + 49 x^{4}$
Frobenius angles:  $\pm0.0252087988121$, $\pm0.641457867855$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-3}, \sqrt{-19})\)
Galois group:  $V_4$

This isogeny class is 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.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28 2128 94864 5592384 281904868 13698361600 676907959252 33235963133184 1627638013248016 79783079565506128

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 45 272 2329 16775 116430 821945 5765329 40334384 282442725

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.