Properties

Label 2.167.a_hi
Base Field $\F_{167}$
Dimension $2$
Ordinary No
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{167}$
Dimension:  $2$
Weil polynomial:  $( 1 - 12 x + 167 x^{2} )( 1 + 12 x + 167 x^{2} )$
Frobenius angles:  $\pm0.346308130027$, $\pm0.653691869973$
Angle rank:  $1$ (numerical)
Jacobians:  6375

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 6375 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28080 788486400 21691952558640 604997729856000000 16871927924959158308400 470540805806288442638649600 13122923468187020838031023741360 365985214017917247315715286016000000 10206961594320420340222156756888886201520 284661951905016649470981112183772749510560000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 168 28270 4657464 777835678 129891985608 21691943520910 3622557586593624 604967119297872958 101029508532509551848 16871927924989221458350

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{167}$
The isogeny class factors as 1.167.am $\times$ 1.167.m and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
Endomorphism algebra over $\overline{\F}_{167}$
The base change of $A$ to $\F_{167^{2}}$ is 1.27889.hi 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-131}) \)$)$
All geometric endomorphisms are defined over $\F_{167^{2}}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.167.ay_sk$2$(not in LMFDB)
2.167.y_sk$2$(not in LMFDB)
2.167.a_ahi$4$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.167.ay_sk$2$(not in LMFDB)
2.167.y_sk$2$(not in LMFDB)
2.167.a_ahi$4$(not in LMFDB)
2.167.am_ax$6$(not in LMFDB)
2.167.m_ax$6$(not in LMFDB)