Properties

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

Learn more about

Invariants

Base field:  $\F_{7}$
Dimension:  $2$
Weil polynomial:  $1 - 6 x + 18 x^{2} - 42 x^{3} + 49 x^{4}$
Frobenius angles:  $\pm0.0461154155528$, $\pm0.453884584447$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(i, \sqrt{5})\)
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
$A(\F_{q^r})$ 20 2320 111620 5382400 276390500 13841326480 678702544820 33210785894400 1627783961277620 79792266845818000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 50 326 2238 16442 117650 824126 5760958 40338002 282475250

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.