Properties

Label 2.83.abe_pb
Base Field $\F_{83}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{83}$
Dimension:  $2$
L-polynomial:  $( 1 - 15 x + 83 x^{2} )^{2}$
Frobenius angles:  $\pm0.192168636682$, $\pm0.192168636682$
Angle rank:  $1$ (numerical)
Jacobians:  18

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 18 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4761 46662561 327353333904 2253269789767161 15517022622579317961 106890670758419443374336 736365527610609821192597169 5072820248900876298544704875625 34946658826054520474617686195605136 240747533885956964146479803383446900321

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 54 6772 572508 47478916 3939289794 326942401318 27136060729398 2252292209915908 186940254125792484 15516041171924154772

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The isogeny class factors as 1.83.ap 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-107}) \)$)$
All geometric endomorphisms are defined over $\F_{83}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.83.a_ach$2$(not in LMFDB)
2.83.be_pb$2$(not in LMFDB)
2.83.p_fm$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.83.a_ach$2$(not in LMFDB)
2.83.be_pb$2$(not in LMFDB)
2.83.p_fm$3$(not in LMFDB)
2.83.a_ch$4$(not in LMFDB)
2.83.ap_fm$6$(not in LMFDB)