Properties

Label 2.61.ay_kc
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:  $( 1 - 14 x + 61 x^{2} )( 1 - 10 x + 61 x^{2} )$
Frobenius angles:  $\pm0.146275019398$, $\pm0.278857938376$
Angle rank:  $2$ (numerical)
Jacobians:  60

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 60 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2496 13658112 51667761600 191830914662400 713391542560721856 2654358551939349964800 9876832628316327858565056 36751694451781971901847961600 136753054296555381088572946814400 508858110709178338057023579214374912

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 38 3670 227630 13854766 844653878 51520560262 3142742866238 191707316101726 11694146217341510 713342913190197430

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{61}$
The isogeny class factors as 1.61.ao $\times$ 1.61.ak 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.ae_as$2$(not in LMFDB)
2.61.e_as$2$(not in LMFDB)
2.61.y_kc$2$(not in LMFDB)
2.61.aj_ei$3$(not in LMFDB)
2.61.d_ai$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.61.ae_as$2$(not in LMFDB)
2.61.e_as$2$(not in LMFDB)
2.61.y_kc$2$(not in LMFDB)
2.61.aj_ei$3$(not in LMFDB)
2.61.d_ai$3$(not in LMFDB)
2.61.aba_le$4$(not in LMFDB)
2.61.ac_abu$4$(not in LMFDB)
2.61.c_abu$4$(not in LMFDB)
2.61.ba_le$4$(not in LMFDB)
2.61.ax_js$6$(not in LMFDB)
2.61.al_fc$6$(not in LMFDB)
2.61.ad_ai$6$(not in LMFDB)
2.61.j_ei$6$(not in LMFDB)
2.61.l_fc$6$(not in LMFDB)
2.61.x_js$6$(not in LMFDB)
2.61.az_ks$12$(not in LMFDB)
2.61.an_fe$12$(not in LMFDB)
2.61.al_eg$12$(not in LMFDB)
2.61.ab_abi$12$(not in LMFDB)
2.61.b_abi$12$(not in LMFDB)
2.61.l_eg$12$(not in LMFDB)
2.61.n_fe$12$(not in LMFDB)
2.61.z_ks$12$(not in LMFDB)