Properties

Label 2.139.abo_zr
Base Field $\F_{139}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{139}$
Dimension:  $2$
L-polynomial:  $1 - 40 x + 667 x^{2} - 5560 x^{3} + 19321 x^{4}$
Frobenius angles:  $\pm0.0475884439062$, $\pm0.249808207721$
Angle rank:  $2$ (numerical)
Number field:  4.0.6630800.1
Galois group:  $D_{4}$
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
$A(\F_{q^r})$ 14389 368200121 7210829155204 139356170081010425 2692451633415469149829 52020845005694654997376016 1005095134186518923102745743389 19419444423218958154686920312136425 375203088287725290220773323986290514084 7249298871862130579254444504569908289329241

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 100 19056 2684980 373307748 51888833700 7212546081246 1002544292140540 139353666191791428 19370159734200075820 2692452204188460299056

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
The endomorphism algebra of this simple isogeny class is 4.0.6630800.1.
All geometric endomorphisms are defined over $\F_{139}$.

Base change

This is a primitive isogeny class.

Twists

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