# Properties

 Label 2.113.abl_vw Base Field $\F_{113}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian No

## 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.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 9120 160110720 2081740976640 26588232733708800 339464891539244445600 4334534600830007748894720 55347537733267339053932318880 706732561846563865874710464153600 9024267966932536029180016961922961920 115230877638184958505327536299643139177600

 $r$ 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.
 Twist Extension Degree Common 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)