# Properties

 Label 2.107.abj_ua Base Field $\F_{107}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{107}$ Dimension: $2$ L-polynomial: $( 1 - 18 x + 107 x^{2} )( 1 - 17 x + 107 x^{2} )$ Frobenius angles: $\pm0.164078095836$, $\pm0.193011390838$ 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 $A(\F_{q^r})$ 8190 128992500 1501333044120 17185541782500000 196721244968829030450 2252198494309678944120000 25785346971800138708309417730 295216376735636292319789770000000 3379932272717495716714823501282999160 38696844617114470430689289392348012312500

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 73 11265 1225534 131107673 14025952883 1500734953170 160578181710929 17181861907684273 1838459210780173018 196715135689573083825

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
 The isogeny class factors as 1.107.as $\times$ 1.107.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 $\F_{107}$.

## 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 2.107.ab_ado $2$ (not in LMFDB) 2.107.b_ado $2$ (not in LMFDB) 2.107.bj_ua $2$ (not in LMFDB)