Properties

Label 2.83.abk_sw
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:  $( 1 - 18 x + 83 x^{2} )^{2}$
Frobenius angles:  $\pm0.0496118990883$, $\pm0.0496118990883$
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
$A(\F_{q^r})$ 4356 45319824 325399511844 2251230714602496 15515337706155211716 106889563803136084469136 736365002320757424498321636 5072820162870579714748580511744 34946658985415969361029626940784516 240747534120087751567660403032270932624

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 48 6574 569088 47435950 3938862048 326939015518 27136041371760 2252292171719134 186940254978265104 15516041187013750414

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The isogeny class factors as 1.83.as 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-2}) \)$)$
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_agc$2$(not in LMFDB)
2.83.bk_sw$2$(not in LMFDB)
2.83.s_jh$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.83.a_agc$2$(not in LMFDB)
2.83.bk_sw$2$(not in LMFDB)
2.83.s_jh$3$(not in LMFDB)
2.83.a_gc$4$(not in LMFDB)
2.83.as_jh$6$(not in LMFDB)
2.83.ae_i$8$(not in LMFDB)
2.83.e_i$8$(not in LMFDB)