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

• Label: 2.73.u_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:	$\pm0.698986253580$, $\pm0.698986253580$
Angle rank:	$1$ (numerical)
Jacobians:	$62$
Cyclic group of points:	no
Non-cyclic primes:	$2, 3, 7$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$7056$	$28901376$	$150410557584$	$806945377222656$	$4297631845759425936$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$94$	$5422$	$386638$	$28415326$	$2073074494$	$151332950158$	$11047411068718$	$806460059555518$	$58871586115531294$	$4297625837991639022$

Jacobians and polarizations

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

• $y^2=70 x^6+27 x^5+17 x^4+50 x^3+17 x^2+27 x+70$
• $y^2=7 x^6+19 x^5+67 x^4+43 x^3+21 x^2+64 x+65$
• $y^2=x^6+23 x^5+12 x^4+6 x^3+45 x^2+48 x+52$
• $y^2=49 x^6+53 x^5+67 x^4+34 x^3+67 x^2+53 x+49$
• $y^2=57 x^6+2 x^5+60 x^4+14 x^3+7 x^2+36 x+54$
• $y^2=62 x^6+72 x^5+13 x^4+47 x^3+18 x^2+30 x+27$
• $y^2=46 x^6+25 x^5+58 x^4+59 x^3+58 x^2+25 x+46$
• $y^2=19 x^6+60 x^5+14 x^4+10 x^3+13 x^2+13 x+71$
• $y^2=30 x^6+16 x^5+57 x^4+29 x^3+57 x^2+16 x+30$
• $y^2=15 x^6+46 x^5+11 x^4+28 x^3+11 x^2+46 x+15$
• $y^2=54 x^6+72 x^5+56 x^4+54 x^3+4 x^2+43 x+19$
• $y^2=15 x^6+26 x^5+67 x^4+43 x^3+67 x^2+26 x+15$
• $y^2=46 x^6+47 x^5+56 x^4+18 x^3+29 x^2+13 x+65$
• $y^2=10 x^6+48 x^5+7 x^4+62 x^3+7 x^2+48 x+10$
• $y^2=5 x^6+56 x^4+56 x^2+5$
• $y^2=65 x^6+11 x^5+65 x^4+11 x^3+65 x^2+11 x+65$
• $y^2=36 x^6+47 x^4+47 x^2+36$
• $y^2=42 x^6+56 x^5+65 x^4+43 x^3+65 x^2+56 x+42$
• $y^2=43 x^6+x^5+36 x^4+24 x^3+36 x^2+x+43$
• $y^2=x^6+72$
• and

• $y^2=x^6+x^3+1$
• $y^2=36 x^6+12 x^5+49 x^4+20 x^3+57 x^2+54 x+35$
• $y^2=12 x^6+50 x^5+71 x^4+x^3+30 x^2+56 x+54$
• $y^2=70 x^6+67 x^5+16 x^4+53 x^3+16 x^2+67 x+70$
• $y^2=64 x^6+27 x^5+39 x^4+18 x^3+29 x^2+24 x+24$
• $y^2=18 x^6+22 x^5+50 x^4+12 x^3+41 x^2+68 x+17$
• $y^2=35 x^6+27 x^5+44 x^4+54 x^3+45 x^2+14 x+1$
• $y^2=57 x^6+47 x^4+47 x^2+57$
• $y^2=20 x^6+39 x^5+40 x^4+70 x^3+52 x^2+17 x+60$
• $y^2=6 x^6+10 x^4+10 x^2+6$
• $y^2=52 x^6+31 x^5+66 x^4+5 x^3+66 x^2+31 x+52$
• $y^2=52 x^6+34 x^5+67 x^4+37 x^3+32 x^2+10 x+63$
• $y^2=61 x^6+40 x^5+56 x^4+9 x^3+56 x^2+40 x+61$
• $y^2=27 x^6+55 x^5+62 x^4+13 x^3+4 x^2+65 x+39$
• $y^2=9 x^6+64 x^5+17 x^4+72 x^3+41 x^2+67 x+8$
• $y^2=16 x^6+37 x^5+15 x^4+41 x^3+42 x^2+x+2$
• $y^2=70 x^6+x^5+61 x^4+29 x^3+37 x^2+55 x+27$
• $y^2=60 x^6+52 x^5+9 x^4+10 x^3+4 x^2+31 x+29$
• $y^2=5 x^6+48 x^5+65 x^4+2 x^3+64 x^2+18 x+61$
• $y^2=60 x^6+48 x^5+65 x^4+4 x^3+65 x^2+48 x+60$
• $y^2=19 x^6+19 x^5+4 x^4+59 x^3+41 x^2+48 x+54$
• $y^2=x^6+x^3+72$
• $y^2=47 x^6+51 x^5+28 x^4+17 x^3+28 x^2+51 x+47$
• $y^2=18 x^6+6 x^5+13 x^4+7 x^3+13 x^2+6 x+18$
• $y^2=22 x^6+44 x^4+44 x^2+22$
• $y^2=11 x^5+70 x^4+72 x^3+x^2+37 x+1$
• $y^2=36 x^6+42 x^5+66 x^4+48 x^3+66 x^2+42 x+36$
• $y^2=14 x^6+69 x^5+22 x^4+63 x^3+2 x^2+47 x+36$
• $y^2=59 x^6+43 x^5+62 x^4+22 x^3+62 x^2+43 x+59$
• $y^2=50 x^6+25 x^5+72 x^3+25 x+50$
• $y^2=41 x^6+37 x^5+48 x^4+35 x^3+48 x^2+37 x+41$
• $y^2=69 x^6+52 x^5+56 x^4+55 x^3+43 x^2+22 x+35$
• $y^2=x^6+16 x^3+8$
• $y^2=25 x^6+7 x^5+31 x^4+61 x^3+32 x^2+6 x+8$
• $y^2=9 x^6+x^5+36 x^4+13 x^3+4 x^2+58 x+42$
• $y^2=57 x^6+14 x^5+53 x^4+36 x^3+53 x^2+14 x+57$
• $y^2=23 x^6+9 x^5+51 x^4+15 x^3+51 x^2+9 x+23$
• $y^2=11 x^6+58 x^4+58 x^2+11$
• $y^2=68 x^6+20 x^5+23 x^4+14 x^3+23 x^2+20 x+68$
• $y^2=46 x^6+8 x^5+37 x^4+38 x^3+51 x^2+51 x+35$
• $y^2=16 x^6+67 x^5+32 x^4+67 x^3+32 x^2+67 x+16$
• $y^2=33 x^6+20 x^5+62 x^4+26 x^3+20 x^2+45 x+11$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{73}$

The isogeny class factors as 1.73.k^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.au_jm	$2$	(not in LMFDB)
2.73.a_bu	$2$	(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.o_hn	$3$	(not in LMFDB)
2.73.r_ii	$3$	(not in LMFDB)