Properties

Label 2.83.abf_pj
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:  $1 - 31 x + 399 x^{2} - 2573 x^{3} + 6889 x^{4}$
Frobenius angles:  $\pm0.0177383414019$, $\pm0.251888863097$
Angle rank:  $2$ (numerical)
Number field:  4.0.145493.1
Galois group:  $D_{4}$
Jacobians:  3

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 3 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4685 46348705 326709463535 2252308135425725 15515904909644702800 106889641255220509663705 736364793795425368849505435 5072819892529475099757365830325 34946658789707347453493011297731905 240747534026575025470440128914064454400

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 53 6727 571385 47458659 3939006048 326939252419 27136033687319 2252292051689811 186940253931360455 15516041180986908582

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The endomorphism algebra of this simple isogeny class is 4.0.145493.1.
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.bf_pj$2$(not in LMFDB)