# Properties

 Label 2.137.abu_bex Base Field $\F_{137}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{137}$ Dimension: $2$ L-polynomial: $( 1 - 23 x + 137 x^{2} )^{2}$ Frobenius angles: $\pm0.0596181899068$, $\pm0.0596181899068$ Angle rank: $1$ (numerical) Jacobians: 1

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 1 curves, and hence is principally polarizable:

• $y^2=63x^6+124x^5+73x^4+89x^3+11x^2+83x+39$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 13225 342805225 6597911449600 124078565442015625 2329168914662515605625 43716613681232444917350400 820517645938897686249636277225 15400296209609161061017077242015625 289048159827798674344188497283752857600 5425144911338544739646648745623008982055625

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 92 18260 2565926 352220388 48261203692 6611851804430 905824275416236 124097929865711428 17001416407462575542 2329194047620840229300

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
 The isogeny class factors as 1.137.ax 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-19})$$$)$
All geometric endomorphisms are defined over $\F_{137}$.

## Base change

This is a primitive isogeny class.

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.137.a_ajv $2$ (not in LMFDB) 2.137.bu_bex $2$ (not in LMFDB) 2.137.x_pc $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.137.a_ajv $2$ (not in LMFDB) 2.137.bu_bex $2$ (not in LMFDB) 2.137.x_pc $3$ (not in LMFDB) 2.137.a_jv $4$ (not in LMFDB) 2.137.ax_pc $6$ (not in LMFDB)