Properties

Label 2.7.ae_i
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:  $1 - 4 x + 8 x^{2} - 28 x^{3} + 49 x^{4}$
Frobenius angles:  $\pm0.0704914820143$, $\pm0.570491482014$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(i, \sqrt{10})\)
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
$A(\F_{q^r})$ 26 2340 101114 5475600 284431706 13841495460 676699584314 33243988377600 1629091518163226 79792266455518500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 50 292 2278 16924 117650 821692 5766718 40370404 282475250

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.