Properties

Label 2.113.abj_ub
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:  $1 - 35 x + 521 x^{2} - 3955 x^{3} + 12769 x^{4}$
Frobenius angles:  $\pm0.0623216346094$, $\pm0.268275041768$
Angle rank:  $2$ (numerical)
Number field:  4.0.107725.1
Galois group:  $D_{4}$
Jacobians:  18

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 18 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 9301 160730581 2081900207869 26585545472686981 339456339200985339136 4334518753400214773026501 55347517337946966693927314989 706732544870326268364769242070725 9024267964383938840425425812640641461 115230877658749142849804442783417366532096

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 79 12587 1442863 163054131 18424330094 2081949664763 235260513494183 26584441635303523 3004041937723173559 339456739026145333022

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The endomorphism algebra of this simple isogeny class is 4.0.107725.1.
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_ub$2$(not in LMFDB)