Properties

Label 2.83.abc_nh
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:  $1 - 28 x + 345 x^{2} - 2324 x^{3} + 6889 x^{4}$
Frobenius angles:  $\pm0.0329882270638$, $\pm0.317642648029$
Angle rank:  $2$ (numerical)
Number field:  4.0.240737.1
Galois group:  $C_4$
Jacobians:  8

This isogeny class is simple and geometrically 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 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4883 46813321 326971383344 2252125254006761 15515476387668989323 106889346194794976726272 736364835940984147838263859 5072820182088518249708172746633 34946659089208377394461792169018928 240747534164742607477436929321333583641

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 56 6796 571844 47454804 3938897256 326938349926 27136035240440 2252292180251748 186940255533482108 15516041189891730396

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The endomorphism algebra of this simple isogeny class is 4.0.240737.1.
All geometric endomorphisms are defined over $\F_{83}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.83.bc_nh$2$(not in LMFDB)