Properties

Label 2.13.ah_bc
Base Field $\F_{13}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{13}$
Dimension:  $2$
Weil polynomial:  $1 - 7 x + 28 x^{2} - 91 x^{3} + 169 x^{4}$
Frobenius angles:  $\pm0.120377326548$, $\pm0.486822699267$
Angle rank:  $2$ (numerical)
Number field:  4.0.154652.1
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
$A(\F_{q^r})$ 100 29600 4769200 805712000 137908520500 23332299929600 3938535727702900 665418825721664000 112456721449576759600 19005139601246920068000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 7 177 2170 28209 371427 4833894 62766991 815733441 10604623330 137859767257

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.