Properties

Label 2.113.abj_uc
Base field $\F_{113}$
Dimension $2$
$p$-rank $2$
Ordinary Yes
Supersingular No
Simple Yes
Geometrically simple Yes
Primitive Yes
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{113}$
Dimension:  $2$
L-polynomial:  $1 - 35 x + 522 x^{2} - 3955 x^{3} + 12769 x^{4}$
Frobenius angles:  $\pm0.0731369855745$, $\pm0.265202456718$
Angle rank:  $2$ (numerical)
Number field:  4.0.9756524.1
Galois group:  $D_{4}$
Jacobians:  12

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 the Jacobians of 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 9302 160757164 2082052074464 26586004349632256 339457290362109832582 4334520254351466206953216 55347519242333845588092641798 706732546925906697638763360041984 9024267966509170372752157755370908896 115230877661295625361797743513464645122924

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 79 12589 1442968 163056945 18424381719 2081950385698 235260521588983 26584441712626209 3004041938430630904 339456739033646973789

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The endomorphism algebra of this simple isogeny class is 4.0.9756524.1.
All geometric endomorphisms are defined over $\F_{113}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.113.bj_uc$2$(not in LMFDB)