Properties

Label 2.113.abj_ua
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:  $( 1 - 21 x + 113 x^{2} )( 1 - 14 x + 113 x^{2} )$
Frobenius angles:  $\pm0.0498602789898$, $\pm0.271189304635$
Angle rank:  $2$ (numerical)
Jacobians:  30

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 contains the Jacobians of 30 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 9300 160704000 2081748344400 26585085945600000 339455381592115816500 4334517219558479671296000 55347515318282448289094330100 706732542503439792704142105600000 9024267961570017235282993028796613200 115230877654904057098829218314924849600000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 79 12585 1442758 163051313 18424278119 2081948928030 235260504909383 26584441546270753 3004041936786461734 339456739014818158425

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The isogeny class factors as 1.113.av $\times$ 1.113.ao 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 are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.113.ah_acq$2$(not in LMFDB)
2.113.h_acq$2$(not in LMFDB)
2.113.bj_ua$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.113.ah_acq$2$(not in LMFDB)
2.113.h_acq$2$(not in LMFDB)
2.113.bj_ua$2$(not in LMFDB)
2.113.abl_vq$4$(not in LMFDB)
2.113.af_aeg$4$(not in LMFDB)
2.113.f_aeg$4$(not in LMFDB)
2.113.bl_vq$4$(not in LMFDB)