Properties

Label 2.61.aba_lf
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:  $( 1 - 13 x + 61 x^{2} )^{2}$
Frobenius angles:  $\pm0.187058313935$, $\pm0.187058313935$
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
$A(\F_{q^r})$ 2401 13505625 51603482896 191852278655625 713439077260126441 2654392338040343040000 9876845093953033243628161 36751693974496820269376855625 136753050082996873096978549415056 508858107406189308538120649816015625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 36 3628 227346 13856308 844710156 51521216038 3142746832716 191707313612068 11694145857028026 713342908559901148

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{61}$
The isogeny class factors as 1.61.an 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_abv$2$(not in LMFDB)
2.61.ba_lf$2$(not in LMFDB)
2.61.ao_ff$3$(not in LMFDB)
2.61.ac_et$3$(not in LMFDB)
2.61.b_aci$3$(not in LMFDB)
2.61.n_ee$3$(not in LMFDB)
2.61.bc_mg$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.61.a_abv$2$(not in LMFDB)
2.61.ba_lf$2$(not in LMFDB)
2.61.ao_ff$3$(not in LMFDB)
2.61.ac_et$3$(not in LMFDB)
2.61.b_aci$3$(not in LMFDB)
2.61.n_ee$3$(not in LMFDB)
2.61.bc_mg$3$(not in LMFDB)
2.61.a_bv$4$(not in LMFDB)
2.61.abc_mg$6$(not in LMFDB)
2.61.abb_ls$6$(not in LMFDB)
2.61.ap_fg$6$(not in LMFDB)
2.61.an_ee$6$(not in LMFDB)
2.61.am_ef$6$(not in LMFDB)
2.61.ab_aci$6$(not in LMFDB)
2.61.a_acw$6$(not in LMFDB)
2.61.a_er$6$(not in LMFDB)
2.61.c_et$6$(not in LMFDB)
2.61.m_ef$6$(not in LMFDB)
2.61.o_ff$6$(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_cw$12$(not in LMFDB)