Properties

 Label 2.23.am_cu Base Field $\F_{23}$ Dimension $2$ $p$-rank $2$ Principally polarizable Contains a Jacobian

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Invariants

 Base field: $\F_{23}$ Dimension: $2$ Weil polynomial: $1 - 12 x + 72 x^{2} - 276 x^{3} + 529 x^{4}$ Frobenius angles: $\pm0.095603857529$, $\pm0.404396142471$ Angle rank: $1$ (numerical) Number field: $$\Q(i, \sqrt{10})$$ 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.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 314 279460 148474586 78097891600 41391692364794 21914624696975140 11593380278594010266 6132675219602112921600 3244153234658230621747514 1716155831334506630544686500

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 12 530 12204 279078 6430932 148035890 3404985204 78311812798 1801153952172 41426511213650

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.