Properties

 Label 2.1024.aer_ill 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: $1 - 121 x + 5705 x^{2} - 123904 x^{3} + 1048576 x^{4}$ Frobenius angles: $\pm0.0734698624279$, $\pm0.130488439581$ Angle rank: $2$ (numerical) Number field: 4.0.2618993.1 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 $A(\F_{q^r})$ 930257 1096128334899 1152843814048828148 1208924587566587439268227 1267650604462243841032602086297 1329227997249390063766652713552821504 1393796574989951564768308392279046174875761 1461501637334259815975388917555633522130541821123 1532495540866005481064365841508478940166285214630716116 1606938044258993836851167708914555814099936558265352980411459

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 904 1045346 1073669467 1099510507234 1125899910603184 1152921505877075855 1180591620786688110904 1208925819617405935461250 1237940039285474481970806091 1267650600228232210874306919986

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
 The endomorphism algebra of this simple isogeny class is 4.0.2618993.1.
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.er_ill $2$ (not in LMFDB)