Properties

Label 2.113.abj_uh
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:  $1 - 35 x + 527 x^{2} - 3955 x^{3} + 12769 x^{4}$
Frobenius angles:  $\pm0.119021368587$, $\pm0.246263793614$
Angle rank:  $2$ (numerical)
Number field:  4.0.5869269.1
Galois group:  $D_{4}$
Jacobians:  8

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 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 9307 160890109 2082811454539 26588288982671941 339461949451971424432 4334527266625128481016341 55347527047207899179159134963 706732552620303916476453942180069 9024267967223541977532848443959922171 115230877656109756241791553789951788397824

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 79 12599 1443493 163070955 18424634594 2081953753823 235260554764433 26584441926826579 3004041938668434379 339456739018370007614

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The endomorphism algebra of this simple isogeny class is 4.0.5869269.1.
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_uh$2$(not in LMFDB)