Properties

Label 2.113.abj_ui
Base Field $\F_{113}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{113}$
Dimension:  $2$
L-polynomial:  $1 - 35 x + 528 x^{2} - 3955 x^{3} + 12769 x^{4}$
Frobenius angles:  $\pm0.128108777714$, $\pm0.241301548635$
Angle rank:  $2$ (numerical)
Number field:  4.0.1070456.1
Galois group:  $D_{4}$
Jacobians:  24

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 24 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 9308 160916704 2082963340016 26588743959030656 339462861926875359868 4334528570758275057965056 55347528267191492908233054332 706732552859681664102086761270784 9024267965467454146586146855606079984 115230877651798183657848064192234873414624

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 79 12601 1443598 163073745 18424684119 2081954380222 235260559950103 26584441935831009 3004041938083859374 339456739005668617161

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The endomorphism algebra of this simple isogeny class is 4.0.1070456.1.
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_ui$2$(not in LMFDB)