Properties

Label 2.113.abk_vd
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:  $( 1 - 19 x + 113 x^{2} )( 1 - 17 x + 113 x^{2} )$
Frobenius angles:  $\pm0.148111132014$, $\pm0.205038125192$
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
$A(\F_{q^r})$ 9215 160552945 2082577615040 26589151546802425 339465155397052785575 4334533248392388142366720 55347534092758806454278261815 706732556228489513136981543453225 9024267961176194529218518960111267520 115230877635623386408858265089680371428225

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 78 12572 1443330 163076244 18424808598 2081956626974 235260584712294 26584442062552036 3004041936655364130 339456738958019549132

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The isogeny class factors as 1.113.at $\times$ 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.ac_adt$2$(not in LMFDB)
2.113.c_adt$2$(not in LMFDB)
2.113.bk_vd$2$(not in LMFDB)