Properties

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

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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:

Point counts of the abelian variety

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

Point counts of the curve

$r$ 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.
TwistExtension DegreeCommon 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.
TwistExtension DegreeCommon 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)