Properties

Label 2.113.abl_vq
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:  $( 1 - 21 x + 113 x^{2} )( 1 - 16 x + 113 x^{2} )$
Frobenius angles:  $\pm0.0498602789898$, $\pm0.228810695365$
Angle rank:  $2$ (numerical)
Jacobians:  9

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 9 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 9114 159950700 2080777274856 26585085945600000 339457692681824264394 4334521892328811430956800 55347519903935137138188406506 706732542503439792704142105600000 9024267953265503348608310378133973224 115230877639453623098469019219973722867500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 77 12525 1442084 163051313 18424403557 2081951172450 235260524401189 26584441546270753 3004041934022015012 339456738969302980125

Decomposition and endomorphism algebra

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