Properties

Label 2.61.abb_lq
Base Field $\F_{61}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{61}$
Dimension:  $2$
L-polynomial:  $( 1 - 15 x + 61 x^{2} )( 1 - 12 x + 61 x^{2} )$
Frobenius angles:  $\pm0.0900194921159$, $\pm0.221142061624$
Angle rank:  $2$ (numerical)
Jacobians:  5

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 contains the Jacobians of 5 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2350 13390300 51483762400 191759808240000 713381657019583750 2654364018363346643200 9876835289341756339168150 36751693269957700872277440000 136753052405163214028601309253600 508858109817094550832148042994357500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 35 3597 226820 13849633 844642175 51520666362 3142743712955 191707309936993 11694146055603140 713342911939629477

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{61}$
The isogeny class factors as 1.61.ap $\times$ 1.61.am 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 $\F_{61}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.61.ad_acg$2$(not in LMFDB)
2.61.d_acg$2$(not in LMFDB)
2.61.bb_lq$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.61.ad_acg$2$(not in LMFDB)
2.61.d_acg$2$(not in LMFDB)
2.61.bb_lq$2$(not in LMFDB)
2.61.az_km$4$(not in LMFDB)
2.61.af_abc$4$(not in LMFDB)
2.61.f_abc$4$(not in LMFDB)
2.61.z_km$4$(not in LMFDB)