Properties

Label 2.73.abi_qt
Base Field $\F_{73}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{73}$
Dimension:  $2$
L-polynomial:  $( 1 - 17 x + 73 x^{2} )^{2}$
Frobenius angles:  $\pm0.0323195869136$, $\pm0.0323195869136$
Angle rank:  $1$ (numerical)
Jacobians:  0

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 is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3249 26904969 150410557584 805904150179401 4297295902545728289 22901854924751191474176 122044902726184491696323409 650377816805538919039567495689 3465863686653762090165171775356816 18469587753342914475861201990604436649

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 40 5044 386638 28378660 2072912440 151332950158 11047388443096 806460013759684 58871586115531294 4297625825330846164

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The isogeny class factors as 1.73.ar 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-3}) \)$)$
All geometric endomorphisms are defined over $\F_{73}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.73.a_afn$2$(not in LMFDB)
2.73.bi_qt$2$(not in LMFDB)
2.73.ak_bb$3$(not in LMFDB)
2.73.ah_ay$3$(not in LMFDB)
2.73.o_hn$3$(not in LMFDB)
2.73.r_ii$3$(not in LMFDB)
2.73.u_jm$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.73.a_afn$2$(not in LMFDB)
2.73.bi_qt$2$(not in LMFDB)
2.73.ak_bb$3$(not in LMFDB)
2.73.ah_ay$3$(not in LMFDB)
2.73.o_hn$3$(not in LMFDB)
2.73.r_ii$3$(not in LMFDB)
2.73.u_jm$3$(not in LMFDB)
2.73.a_fn$4$(not in LMFDB)
2.73.abb_me$6$(not in LMFDB)
2.73.ay_kf$6$(not in LMFDB)
2.73.au_jm$6$(not in LMFDB)
2.73.ar_ii$6$(not in LMFDB)
2.73.ao_hn$6$(not in LMFDB)
2.73.ad_cy$6$(not in LMFDB)
2.73.a_bu$6$(not in LMFDB)
2.73.a_dt$6$(not in LMFDB)
2.73.d_cy$6$(not in LMFDB)
2.73.h_ay$6$(not in LMFDB)
2.73.k_bb$6$(not in LMFDB)
2.73.y_kf$6$(not in LMFDB)
2.73.bb_me$6$(not in LMFDB)
2.73.a_adt$12$(not in LMFDB)
2.73.a_abu$12$(not in LMFDB)