Properties

Label 2.61.abc_mg
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:  $( 1 - 14 x + 61 x^{2} )^{2}$
Frobenius angles:  $\pm0.146275019398$, $\pm0.146275019398$
Angle rank:  $1$ (numerical)
Jacobians:  8

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 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2304 13307904 51438240000 191761786404864 713408161597565184 2654392338040343040000 9876854756003829518778624 36751702992076970789635620864 136753055598099213272567463840000 508858109901056851995688231679299584

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 34 3574 226618 13849774 844673554 51521216038 3142749907114 191707360650334 11694146328640258 713342912057332054

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{61}$
The isogeny class factors as 1.61.ao 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-3}) \)$)$
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.a_acw$2$(not in LMFDB)
2.61.bc_mg$2$(not in LMFDB)
2.61.an_ee$3$(not in LMFDB)
2.61.ab_aci$3$(not in LMFDB)
2.61.c_et$3$(not in LMFDB)
2.61.o_ff$3$(not in LMFDB)
2.61.ba_lf$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.61.a_acw$2$(not in LMFDB)
2.61.bc_mg$2$(not in LMFDB)
2.61.an_ee$3$(not in LMFDB)
2.61.ab_aci$3$(not in LMFDB)
2.61.c_et$3$(not in LMFDB)
2.61.o_ff$3$(not in LMFDB)
2.61.ba_lf$3$(not in LMFDB)
2.61.a_cw$4$(not in LMFDB)
2.61.abb_ls$6$(not in LMFDB)
2.61.aba_lf$6$(not in LMFDB)
2.61.ap_fg$6$(not in LMFDB)
2.61.ao_ff$6$(not in LMFDB)
2.61.am_ef$6$(not in LMFDB)
2.61.ac_et$6$(not in LMFDB)
2.61.a_abv$6$(not in LMFDB)
2.61.a_er$6$(not in LMFDB)
2.61.b_aci$6$(not in LMFDB)
2.61.m_ef$6$(not in LMFDB)
2.61.n_ee$6$(not in LMFDB)
2.61.p_fg$6$(not in LMFDB)
2.61.bb_ls$6$(not in LMFDB)
2.61.a_aer$12$(not in LMFDB)
2.61.a_bv$12$(not in LMFDB)