Properties

Label 2.137.abs_bde
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:  $( 1 - 22 x + 137 x^{2} )^{2}$
Frobenius angles:  $\pm0.111017258455$, $\pm0.111017258455$
Angle rank:  $1$ (numerical)
Jacobians:  10

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 10 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 13456 344473600 6603604783504 124093307453440000 2329201350436737613456 43716676977327384006246400 820517757336797747775065578384 15400296386442587467088398909440000 289048160076064916232496775763861440656 5425144911627714989937535120907093616640000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 94 18350 2568142 352262238 48261875774 6611861377550 905824398395822 124097931290662078 17001416422065255454 2329194047744990576750

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
The isogeny class factors as 1.137.aw 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-1}) \)$)$
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_aic$2$(not in LMFDB)
2.137.bs_bde$2$(not in LMFDB)
2.137.w_nj$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.137.a_aic$2$(not in LMFDB)
2.137.bs_bde$2$(not in LMFDB)
2.137.w_nj$3$(not in LMFDB)
2.137.abe_ri$4$(not in LMFDB)
2.137.aq_na$4$(not in LMFDB)
2.137.ao_du$4$(not in LMFDB)
2.137.a_ic$4$(not in LMFDB)
2.137.o_du$4$(not in LMFDB)
2.137.q_na$4$(not in LMFDB)
2.137.be_ri$4$(not in LMFDB)
2.137.aw_nj$6$(not in LMFDB)
2.137.a_agu$8$(not in LMFDB)
2.137.a_gu$8$(not in LMFDB)
2.137.ai_acv$12$(not in LMFDB)
2.137.i_acv$12$(not in LMFDB)