Properties

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

Invariants

 Base field: $\F_{13}$ Dimension: $2$ Weil polynomial: $1 - 7 x + 31 x^{2} - 91 x^{3} + 169 x^{4}$ Frobenius angles: $\pm0.171237405357$, $\pm0.464284369344$ Angle rank: $2$ (numerical) Number field: 4.0.589541.1 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.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 103 30797 4908259 812332469 138024863248 23335821681341 3938886321816451 665406078106775525 112453276162713512311 19004944842626077700352

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 7 183 2233 28443 371742 4834623 62772577 815717811 10604298439 137858354518

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.