Abelian variety isogeny class 2.73.o_hn over $\F_{73}$

• Label: 2.73.o_hn
• Base field: $\F_{73}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{73}$
Dimension:	$2$
L-polynomial:	$( 1 + 7 x + 73 x^{2} )^{2}$
	$1 + 14 x + 195 x^{2} + 1022 x^{3} + 5329 x^{4}$
Frobenius angles:	$\pm0.634347079753$, $\pm0.634347079753$
Angle rank:	$1$ (numerical)
Jacobians:	$43$
Cyclic group of points:	no
Non-cyclic primes:	$3$

This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

$p$-rank:	$2$
Slopes:	$[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$6561$	$29452329$	$150410557584$	$806531089059081$	$4297949765682377841$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$88$	$5524$	$386638$	$28400740$	$2073227848$	$151332950158$	$11047396045480$	$806460202367044$	$58871586115531294$	$4297625825788187764$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 43 curves (of which all are hyperelliptic):

• $y^2=41 x^6+x^5+41 x^4+9 x^3+55 x^2+16 x+4$
• $y^2=16 x^6+66 x^5+68 x^4+x^3+72 x^2+33 x+4$
• $y^2=46 x^6+64 x^5+27 x^4+12 x^3+66 x^2+14 x+31$
• $y^2=35 x^6+34 x^5+64 x^4+53 x^3+58 x^2+4 x+56$
• $y^2=x^6+71 x^3+65$
• $y^2=33 x^6+8 x^5+67 x^4+34 x^3+40 x^2+59 x+55$
• $y^2=x^6+6 x^3+70$
• $y^2=43 x^6+56 x^5+44 x^3+63 x+7$
• $y^2=23 x^6+58 x^5+29 x^4+65 x^3+66 x^2+21 x+41$
• $y^2=41 x^6+64 x^5+56 x^4+27 x^3+35 x^2+31 x+62$
• $y^2=x^6+x^3+9$
• $y^2=32 x^6+60 x^5+61 x^4+22 x^3+44 x^2+7 x+17$
• $y^2=64 x^6+58 x^5+53 x^3+38 x^2+50 x+31$
• $y^2=50 x^6+43 x^5+41 x^4+40 x^3+57 x^2+29 x+61$
• $y^2=62 x^6+28 x^5+57 x^4+6 x^3+56 x^2+46 x+39$
• $y^2=62 x^6+22 x^5+16 x^4+54 x^3+69 x^2+16 x+45$
• $y^2=49 x^6+51 x^5+39 x^4+57 x^3+71 x^2+28 x+44$
• $y^2=32 x^6+26 x^5+9 x^4+x^3+18 x^2+6 x+12$
• $y^2=x^6+57 x^3+65$
• $y^2=67 x^6+36 x^5+48 x^4+31 x^3+9 x^2+64 x+71$
• and

• $y^2=25 x^6+13 x^5+68 x^4+14 x^3+53 x^2+62 x+67$
• $y^2=37 x^6+59 x^5+14 x^4+42 x^3+36 x^2+42 x+21$
• $y^2=4 x^6+38 x^5+35 x^4+69 x^3+38 x^2+38 x+69$
• $y^2=33 x^6+32 x^5+13 x^4+40 x^3+45 x^2+4 x+38$
• $y^2=72 x^6+55 x^5+50 x^4+12 x^3+50 x^2+55 x+72$
• $y^2=58 x^6+29 x^5+71 x^4+21 x^3+71 x^2+29 x+58$
• $y^2=52 x^6+12 x^5+5 x^4+43 x^3+62 x^2+61 x+56$
• $y^2=56 x^6+16 x^5+29 x^4+43 x^3+60 x^2+x+58$
• $y^2=48 x^6+37 x^5+68 x^4+31 x^2+9 x+16$
• $y^2=71 x^6+10 x^5+7 x^4+2 x^3+68 x^2+20 x+55$
• $y^2=34 x^6+34 x^5+15 x^4+47 x^3+17 x^2+56 x+44$
• $y^2=18 x^6+45 x^5+9 x^4+61 x^3+71 x^2+59 x+71$
• $y^2=52 x^6+59 x^5+35 x^4+15 x^3+11 x^2+58 x+10$
• $y^2=3 x^6+32 x^5+6 x^4+15 x^3+3 x^2+8 x+46$
• $y^2=48 x^6+22 x^5+55 x^4+30 x^3+65 x^2+44 x+67$
• $y^2=52 x^6+26 x^5+65 x^4+3 x^3+70 x^2+47 x+17$
• $y^2=65 x^6+59 x^5+28 x^4+35 x^3+53 x^2+45 x+1$
• $y^2=19 x^6+13 x^5+58 x^4+48 x^3+5 x^2+42 x+2$
• $y^2=37 x^6+56 x^5+12 x^4+x^3+32 x^2+17 x+23$
• $y^2=46 x^6+18 x^5+46 x^4+9 x^3+44 x^2+14 x+30$
• $y^2=25 x^6+33 x^5+45 x^4+62 x^3+5 x^2+68 x+48$
• $y^2=8 x^6+21 x^5+17 x^4+69 x^3+26 x^2+13 x+27$
• $y^2=43 x^6+50 x^5+53 x^4+17 x^3+8 x^2+59 x+6$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{73}$.

Endomorphism algebra over $\F_{73}$

The isogeny class factors as 1.73.h^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-3}) \)$)$

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.ao_hn	$2$	(not in LMFDB)
2.73.a_dt	$2$	(not in LMFDB)
2.73.abi_qt	$3$	(not in LMFDB)
2.73.ak_bb	$3$	(not in LMFDB)
2.73.ah_ay	$3$	(not in LMFDB)
2.73.r_ii	$3$	(not in LMFDB)
2.73.u_jm	$3$	(not in LMFDB)