Properties

Label 2.139.abt_bee
Base Field $\F_{139}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{139}$
Dimension:  $2$
L-polynomial:  $( 1 - 23 x + 139 x^{2} )( 1 - 22 x + 139 x^{2} )$
Frobenius angles:  $\pm0.0707251543800$, $\pm0.117174211439$
Angle rank:  $2$ (numerical)
Jacobians:  0

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 13806 364561236 7201681820424 139343158506468384 2692448012954737577826 52020882986543132116867776 1005095263314788523069442152786 19419444688735227776345169435114624 375203088685935935743214232068325511464 7249298872294029907724298389988067273296276

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 95 18865 2681570 373272889 51888763925 7212551347186 1002544420941095 139353668097132529 19370159754758019110 2692452204348871439425

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
The isogeny class factors as 1.139.ax $\times$ 1.139.aw and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{139}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.139.ab_aiu$2$(not in LMFDB)
2.139.b_aiu$2$(not in LMFDB)
2.139.bt_bee$2$(not in LMFDB)
2.139.ap_eu$3$(not in LMFDB)
2.139.ag_acw$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.139.ab_aiu$2$(not in LMFDB)
2.139.b_aiu$2$(not in LMFDB)
2.139.bt_bee$2$(not in LMFDB)
2.139.ap_eu$3$(not in LMFDB)
2.139.ag_acw$3$(not in LMFDB)
2.139.abm_yg$6$(not in LMFDB)
2.139.abd_qq$6$(not in LMFDB)
2.139.g_acw$6$(not in LMFDB)
2.139.p_eu$6$(not in LMFDB)
2.139.bd_qq$6$(not in LMFDB)
2.139.bm_yg$6$(not in LMFDB)