Properties

 Label 2.1024.aeu_isp 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: $( 1 - 63 x + 1024 x^{2} )( 1 - 61 x + 1024 x^{2} )$ Frobenius angles: $\pm0.0563432964760$, $\pm0.0978468837242$ Angle rank: $2$ (numerical)

This isogeny class is not 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 $A(\F_{q^r})$ 927368 1095748353024 1152818322402162104 1208923296386095001088000 1267650549825516476473396268648 1329227995247868036776384634415266816 1393796574926267473599546550408166388980888 1461501637332556272949554010149617462405855232000 1532495540865971855896020359123426120248784657947077704 1606938044258993688597295428201264397117765331367992245115904

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 901 1044983 1073645725 1099509332911 1125899862076021 1152921504141032231 1180591620732745587469 1208925819615996797697631 1237940039285447319776129125 1267650600228232093922623030103

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
 The isogeny class factors as 1.1024.acl $\times$ 1.1024.acj and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ac_acrb $2$ (not in LMFDB) 2.1024.c_acrb $2$ (not in LMFDB) 2.1024.eu_isp $2$ (not in LMFDB)