Properties

Label 2.7.ad_g
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:  $1 - 3 x + 6 x^{2} - 21 x^{3} + 49 x^{4}$
Frobenius angles:  $\pm0.151739874815$, $\pm0.604208870972$
Angle rank:  $2$ (numerical)
Number field:  4.0.62197.1
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
$A(\F_{q^r})$ 32 2560 106112 5785600 290070752 13887938560 678565710176 33278609203200 1628723122905728 79782335941388800

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 53 308 2409 17255 118046 823961 5772721 40361276 282440093

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.