Properties

Label 2.113.abl_vw
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:  $( 1 - 19 x + 113 x^{2} )( 1 - 18 x + 113 x^{2} )$
Frobenius angles:  $\pm0.148111132014$, $\pm0.178616545187$
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
$A(\F_{q^r})$ 9120 160110720 2081740976640 26588232733708800 339464891539244445600 4334534600830007748894720 55347537733267339053932318880 706732561846563865874710464153600 9024267966932536029180016961922961920 115230877638184958505327536299643139177600

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 77 12537 1442750 163070609 18424794277 2081957276574 235260600186661 26584442273881441 3004041938571562910 339456738965565642057

Decomposition and endomorphism algebra

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