Properties

Label 2.7.af_r
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:  $1 - 5 x + 17 x^{2} - 35 x^{3} + 49 x^{4}$
Frobenius angles:  $\pm0.197751856397$, $\pm0.457936209148$
Angle rank:  $2$ (numerical)
Number field:  4.0.4901.1
Galois group:  $D_4$

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
$A(\F_{q^r})$ 27 2889 127089 5746221 284148432 13965683121 679950980253 33212289700629 1627543164886911 79785138039047424

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 3 59 369 2395 16908 118703 825639 5761219 40332033 282450014

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.