Properties

 Label 3.4.aj_bl_ado Base Field $\F_{2^2}$ Dimension $3$ $p$-rank $2$ Does not contain a Jacobian

Invariants

 Base field: $\F_{2^2}$ Dimension: $3$ Weil polynomial: $( 1 - 2 x )^{2}( 1 - 5 x + 13 x^{2} - 20 x^{3} + 16 x^{4} )$ Frobenius angles: $0.0$, $0.0$, $\pm0.140237960897$, $\pm0.38771221219$ Angle rank: $2$ (numerical)

Newton polygon

 $p$-rank: $2$ Slopes: $[0, 0, 1/2, 1/2, 1, 1]$

Point counts

This isogeny class does not contain a Jacobian, and it is unknown whether it is principally polarizable.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 5 2475 236180 14911875 982742625 67339641600 4440454748105 283399125631875 17994211219640180 1149268239963421875

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -4 10 59 226 936 4015 16544 65986 261851 1045250

Decomposition

1.4.ae $\times$ 2.4.af_n

Base change

This is a primitive isogeny class.