Properties

Label 2.139.abo_zw
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:  $1 - 40 x + 672 x^{2} - 5560 x^{3} + 19321 x^{4}$
Frobenius angles:  $\pm0.0989502623149$, $\pm0.232779741831$
Angle rank:  $2$ (numerical)
Number field:  4.0.7430400.5
Galois group:  $D_{4}$
Jacobians:  32

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 32 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 14394 368400036 7212443624874 139363117978544400 2692472389058327844954 52020892632613431560466276 1005095221676157533415778639434 19419444553424793689389820348006400 375203088444584824362740134926086795514 7249298872020332044140368631764524986862116

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 100 19066 2685580 373326358 51889233700 7212552684586 1002544379408140 139353667126146718 19370159742298074820 2692452204247217689306

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
The endomorphism algebra of this simple isogeny class is 4.0.7430400.5.
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_zw$2$(not in LMFDB)