Properties

Label 2.113.abm_wl
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:  $( 1 - 21 x + 113 x^{2} )( 1 - 17 x + 113 x^{2} )$
Frobenius angles:  $\pm0.0498602789898$, $\pm0.205038125192$
Angle rank:  $2$ (numerical)
Jacobians:  6

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 6 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 9021 159536385 2080088593488 26584585616734425 339458180535141361221 4334524059813697535016960 55347523627759087962830460117 706732546273360427175587303877225 9024267954290481694632254660550387792 115230877634826652792380154325682492517425

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 76 12492 1441606 163048244 18424430036 2081952213534 235260540229700 26584441688080036 3004041934363214758 339456738955672464732

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The isogeny class factors as 1.113.av $\times$ 1.113.ar 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.ae_afb$2$(not in LMFDB)
2.113.e_afb$2$(not in LMFDB)
2.113.bm_wl$2$(not in LMFDB)