Properties

 Label 2.1024.aep_ign Base Field $\F_{2^{10}}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

Invariants

 Base field: $\F_{2^{10}}$ Dimension: $2$ L-polynomial: $1 - 119 x + 5577 x^{2} - 121856 x^{3} + 1048576 x^{4}$ Frobenius angles: $\pm0.0603251282655$, $\pm0.159355937826$ Angle rank: $2$ (numerical) Number field: 4.0.3429225.3 Galois group: $D_{4}$

This isogeny class is simple and geometrically 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 $A(\F_{q^r})$ 932179 1096362755091 1152857363814367936 1208925110053359410237379 1267650616804359600913435073899 1329227997196895351241603583176343296 1393796574964398044257401147572085529006579 1461501637332485175379344827498183235678204326979 1532495540865918449115749170039582055215314811008408256 1606938044258990358332138384290913015993757098462013893012451

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 906 1045570 1073682087 1099510982434 1125899921565186 1152921505831543951 1180591620765043437114 1208925819615937987165954 1237940039285404178122594743 1267650600228229466806636618450

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
 The endomorphism algebra of this simple isogeny class is 4.0.3429225.3.
All geometric endomorphisms are defined over $\F_{2^{10}}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.1024.ep_ign $2$ (not in LMFDB)