# Properties

 Label 2.113.abj_um 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: $( 1 - 18 x + 113 x^{2} )( 1 - 17 x + 113 x^{2} )$ Frobenius angles: $\pm0.178616545187$, $\pm0.205038125192$ 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 $A(\F_{q^r})$ 9312 161023104 2083570913664 26590557364056576 339466447350001288032 4334533460385263675375616 55347532022016346219455224928 706732550900638076953098077128704 9024267952508266514186044470728666496 115230877625090943209037627147076919812224

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 79 12609 1444018 163084865 18424878719 2081956728798 235260575910383 26584441862139649 3004041933769942354 339456738926992198689

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
 The isogeny class factors as 1.113.as $\times$ 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.
 Twist Extension Degree Common base change 2.113.ab_adc $2$ (not in LMFDB) 2.113.b_adc $2$ (not in LMFDB) 2.113.bj_um $2$ (not in LMFDB)