Properties

Label 2.61.aba_lb
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:  $( 1 - 15 x + 61 x^{2} )( 1 - 11 x + 61 x^{2} )$
Frobenius angles:  $\pm0.0900194921159$, $\pm0.251304563322$
Angle rank:  $2$ (numerical)
Jacobians:  12

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 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2397 13473537 51532201728 191766494252025 713369242431934077 2654351339185173196800 9876828861175819282487877 36751691936687469312987333225 136753053211936915846625854879488 508858110815275790850534678501921537

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 36 3620 227034 13850116 844627476 51520420262 3142741667556 191707302982276 11694146124592674 713342913338930180

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{61}$
The isogeny class factors as 1.61.ap $\times$ 1.61.al 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 is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.61.ae_abr$2$(not in LMFDB)
2.61.e_abr$2$(not in LMFDB)
2.61.ba_lb$2$(not in LMFDB)