Properties

Label 2.113.abi_te
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:  $1 - 34 x + 498 x^{2} - 3842 x^{3} + 12769 x^{4}$
Frobenius angles:  $\pm0.0361800547850$, $\pm0.292901901285$
Angle rank:  $2$ (numerical)
Number field:  4.0.120224.1
Galois group:  $D_{4}$
Jacobians:  28

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 28 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 9392 161016448 2081900530736 26584274139643904 339453080056439805232 4334514089846454338780800 55347513288750404566140725168 706732543255041012358602415407104 9024267964063164335389990234922758064 115230877654170801900390313275402658956928

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 80 12610 1442864 163046334 18424153200 2081947424770 235260496282640 26584441574542974 3004041937616392592 339456739012658074050

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The endomorphism algebra of this simple isogeny class is 4.0.120224.1.
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.bi_te$2$(not in LMFDB)