Properties

Label 2.139.abr_bcj
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:  $1 - 43 x + 737 x^{2} - 5977 x^{3} + 19321 x^{4}$
Frobenius angles:  $\pm0.0488276070962$, $\pm0.185265935553$
Angle rank:  $2$ (numerical)
Number field:  4.0.368589.1
Galois group:  $D_{4}$
Jacobians:  6

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 6 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 14039 366123081 7206201614537 139351783069244061 2692458192750605660624 52020881963077220947780569 1005095218219601866673843227229 19419444536131486282313517718878549 375203088329197597078858623562025599307 7249298871624660761746683862690195859602176

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 97 18947 2683255 373295995 51888960112 7212551205287 1002544375960357 139353667002050179 19370159736341116855 2692452204100261958102

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
The endomorphism algebra of this simple isogeny class is 4.0.368589.1.
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.br_bcj$2$(not in LMFDB)