Properties

Label 2.139.abn_yu
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:  $1 - 39 x + 644 x^{2} - 5421 x^{3} + 19321 x^{4}$
Frobenius angles:  $\pm0.0512302470248$, $\pm0.267624205263$
Angle rank:  $2$ (numerical)
Number field:  4.0.14321592.1
Galois group:  $D_{4}$
Jacobians:  12

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 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 14506 368829556 7211918601832 139356201880518048 2692447325174472076966 52020834364737421315889344 1005095124858502421737943123638 19419444442267330846062043979620992 375203088377945894339435326435240409608 7249298872042682638569157054840574533816756

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 101 19089 2685386 373307833 51888750671 7212544605906 1002544282836197 139353666328482289 19370159738857786718 2692452204255518893089

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
The endomorphism algebra of this simple isogeny class is 4.0.14321592.1.
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.bn_yu$2$(not in LMFDB)