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

• Label: 2.73.au_jm
• 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:	$( 1 - 10 x + 73 x^{2} )^{2}$
	$1 - 20 x + 246 x^{2} - 1460 x^{3} + 5329 x^{4}$
Frobenius angles:	$\pm0.301013746420$, $\pm0.301013746420$
Angle rank:	$1$ (numerical)
Jacobians:	$62$
Cyclic group of points:	no
Non-cyclic primes:	$2$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$4096$	$28901376$	$152262283264$	$806945377222656$	$4297619821944180736$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$54$	$5422$	$391398$	$28415326$	$2073068694$	$151332950158$	$11047385969478$	$806460059555518$	$58871587301004534$	$4297625837991639022$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 62 curves (of which all are hyperelliptic):

• $y^2=14 x^6+20 x^5+18 x^4+10 x^3+18 x^2+20 x+14$
• $y^2=35 x^6+22 x^5+43 x^4+69 x^3+32 x^2+28 x+33$
• $y^2=5 x^6+42 x^5+60 x^4+30 x^3+6 x^2+21 x+41$
• $y^2=39 x^6+69 x^5+28 x^4+36 x^3+28 x^2+69 x+39$
• $y^2=66 x^6+10 x^5+8 x^4+70 x^3+35 x^2+34 x+51$
• $y^2=18 x^6+68 x^5+65 x^4+16 x^3+17 x^2+4 x+62$
• $y^2=11 x^6+52 x^5+71 x^4+3 x^3+71 x^2+52 x+11$
• $y^2=22 x^6+8 x^5+70 x^4+50 x^3+65 x^2+65 x+63$
• $y^2=4 x^6+7 x^5+66 x^4+72 x^3+66 x^2+7 x+4$
• $y^2=3 x^6+53 x^5+46 x^4+64 x^3+46 x^2+53 x+3$
• $y^2=51 x^6+68 x^5+61 x^4+51 x^3+20 x^2+69 x+22$
• $y^2=3 x^6+49 x^5+28 x^4+67 x^3+28 x^2+49 x+3$
• $y^2=11 x^6+16 x^5+61 x^4+17 x^3+72 x^2+65 x+33$
• $y^2=50 x^6+21 x^5+35 x^4+18 x^3+35 x^2+21 x+50$
• $y^2=25 x^6+61 x^4+61 x^2+25$
• $y^2=33 x^6+55 x^5+33 x^4+55 x^3+33 x^2+55 x+33$
• $y^2=34 x^6+16 x^4+16 x^2+34$
• $y^2=64 x^6+61 x^5+33 x^4+69 x^3+33 x^2+61 x+64$
• $y^2=69 x^6+5 x^5+34 x^4+47 x^3+34 x^2+5 x+69$
• $y^2=5 x^6+68$
• and

• $y^2=5 x^6+5 x^3+5$
• $y^2=51 x^6+17 x^5+39 x^4+4 x^3+26 x^2+40 x+7$
• $y^2=60 x^6+31 x^5+63 x^4+5 x^3+4 x^2+61 x+51$
• $y^2=58 x^6+43 x^5+7 x^4+46 x^3+7 x^2+43 x+58$
• $y^2=28 x^6+62 x^5+49 x^4+17 x^3+72 x^2+47 x+47$
• $y^2=17 x^6+37 x^5+31 x^4+60 x^3+59 x^2+48 x+12$
• $y^2=29 x^6+62 x^5+x^4+51 x^3+6 x^2+70 x+5$
• $y^2=26 x^6+24 x^4+24 x^2+26$
• $y^2=4 x^6+37 x^5+8 x^4+14 x^3+25 x^2+18 x+12$
• $y^2=45 x^6+2 x^4+2 x^2+45$
• $y^2=25 x^6+50 x^5+57 x^4+x^3+57 x^2+50 x+25$
• $y^2=41 x^6+24 x^5+43 x^4+39 x^3+14 x^2+50 x+23$
• $y^2=56 x^6+8 x^5+55 x^4+31 x^3+55 x^2+8 x+56$
• $y^2=62 x^6+56 x^5+18 x^4+65 x^3+20 x^2+33 x+49$
• $y^2=31 x^6+42 x^5+18 x^4+29 x^3+52 x^2+28 x+60$
• $y^2=7 x^6+39 x^5+2 x^4+59 x^3+64 x^2+5 x+10$
• $y^2=14 x^6+44 x^5+56 x^4+35 x^3+22 x^2+11 x+20$
• $y^2=12 x^6+25 x^5+31 x^4+2 x^3+30 x^2+50 x+35$
• $y^2=x^6+68 x^5+13 x^4+15 x^3+42 x^2+62 x+56$
• $y^2=12 x^6+68 x^5+13 x^4+30 x^3+13 x^2+68 x+12$
• $y^2=22 x^6+22 x^5+20 x^4+3 x^3+59 x^2+21 x+51$
• $y^2=5 x^6+5 x^3+68$
• $y^2=16 x^6+36 x^5+67 x^4+12 x^3+67 x^2+36 x+16$
• $y^2=17 x^6+30 x^5+65 x^4+35 x^3+65 x^2+30 x+17$
• $y^2=37 x^6+x^4+x^2+37$
• $y^2=55 x^5+58 x^4+68 x^3+5 x^2+39 x+5$
• $y^2=51 x^6+23 x^5+57 x^4+68 x^3+57 x^2+23 x+51$
• $y^2=70 x^6+53 x^5+37 x^4+23 x^3+10 x^2+16 x+34$
• $y^2=41 x^6+67 x^5+27 x^4+19 x^3+27 x^2+67 x+41$
• $y^2=31 x^6+52 x^5+68 x^3+52 x+31$
• $y^2=52 x^6+22 x^5+68 x^4+7 x^3+68 x^2+22 x+52$
• $y^2=53 x^6+41 x^5+61 x^4+56 x^3+69 x^2+37 x+29$
• $y^2=5 x^6+7 x^3+40$
• $y^2=5 x^6+16 x^5+50 x^4+56 x^3+21 x^2+45 x+60$
• $y^2=45 x^6+5 x^5+34 x^4+65 x^3+20 x^2+71 x+64$
• $y^2=66 x^6+70 x^5+46 x^4+34 x^3+46 x^2+70 x+66$
• $y^2=42 x^6+45 x^5+36 x^4+2 x^3+36 x^2+45 x+42$
• $y^2=46 x^6+70 x^4+70 x^2+46$
• $y^2=72 x^6+4 x^5+63 x^4+32 x^3+63 x^2+4 x+72$
• $y^2=53 x^6+60 x^5+22 x^4+66 x^3+54 x^2+54 x+7$
• $y^2=47 x^6+28 x^5+21 x^4+28 x^3+21 x^2+28 x+47$
• $y^2=19 x^6+27 x^5+18 x^4+57 x^3+27 x^2+6 x+55$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{73}$

The isogeny class factors as 1.73.ak^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.a_bu	$2$	(not in LMFDB)
2.73.u_jm	$2$	(not in LMFDB)
2.73.ar_ii	$3$	(not in LMFDB)
2.73.ao_hn	$3$	(not in LMFDB)
2.73.h_ay	$3$	(not in LMFDB)
2.73.k_bb	$3$	(not in LMFDB)
2.73.bi_qt	$3$	(not in LMFDB)