Properties

Label 2.113.abp_yw
Base Field $\F_{113}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{113}$
Dimension:  $2$
L-polynomial:  $( 1 - 21 x + 113 x^{2} )( 1 - 20 x + 113 x^{2} )$
Frobenius angles:  $\pm0.0498602789898$, $\pm0.110150159186$
Angle rank:  $2$ (numerical)
Jacobians:  0

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8742 158142780 2077106228568 26580296873995200 339453988615119237222 4334522465248154056200960 55347527599422953576376894198 706732558044236598713239306080000 9024267973908129343023634699280953752 115230877659056802621118685457931247403900

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 73 12381 1439536 163021937 18424202513 2081951447634 235260557111681 26584442130853153 3004041940893632128 339456739027051662861

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The isogeny class factors as 1.113.av $\times$ 1.113.au and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ab_ahm$2$(not in LMFDB)
2.113.b_ahm$2$(not in LMFDB)
2.113.bp_yw$2$(not in LMFDB)