# Properties

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

## 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.

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

 $r$ 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.
 Twist Extension Degree Common 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.
 Twist Extension Degree Common 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)