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

• Label: 2.73.aq_ic
• 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:	$( 1 - 8 x + 73 x^{2} )^{2}$
	$1 - 16 x + 210 x^{2} - 1168 x^{3} + 5329 x^{4}$
Frobenius angles:	$\pm0.344915434243$, $\pm0.344915434243$
Angle rank:	$1$ (numerical)
Jacobians:	$42$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$4356$	$29289744$	$152301306564$	$806683601534976$	$4297381015873402116$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$58$	$5494$	$391498$	$28406110$	$2072953498$	$151332707158$	$11047394987050$	$806460174534334$	$58871587627229434$	$4297625831022511414$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 42 curves (of which all are hyperelliptic):

• $y^2=48 x^6+72 x^5+37 x^4+44 x^3+12 x^2+25 x+62$
• $y^2=10 x^6+4 x^5+14 x^4+48 x^3+14 x^2+4 x+10$
• $y^2=33 x^6+43 x^5+14 x^4+44 x^3+43 x^2+62 x+65$
• $y^2=60 x^6+48 x^5+26 x^4+11 x^3+26 x^2+48 x+60$
• $y^2=59 x^6+43 x^5+54 x^4+69 x^3+27 x^2+58 x+54$
• $y^2=59 x^6+9 x^5+51 x^4+11 x^3+5 x^2+41 x+53$
• $y^2=14 x^6+66 x^5+12 x^4+12 x^3+51 x^2+43 x+10$
• $y^2=63 x^6+62 x^5+23 x^4+8 x^3+64 x^2+51 x+63$
• $y^2=34 x^6+24 x^5+11 x^4+19 x^3+11 x^2+24 x+34$
• $y^2=21 x^6+8 x^4+8 x^2+21$
• $y^2=67 x^6+26 x^5+31 x^4+2 x^3+10 x^2+22 x+71$
• $y^2=17 x^6+46 x^5+52 x^4+5 x^3+50 x^2+42 x+47$
• $y^2=11 x^6+4 x^5+59 x^4+4 x^3+21 x+31$
• $y^2=8 x^6+58 x^5+58 x^4+37 x^3+62 x^2+68 x+13$
• $y^2=44 x^6+68 x^5+62 x^3+28 x^2+7 x+30$
• $y^2=34 x^6+58 x^5+31 x^4+30 x^3+46 x^2+66 x+71$
• $y^2=5 x^6+55 x^5+6 x^4+58 x^3+x^2+30 x+19$
• $y^2=58 x^6+3 x^5+16 x^4+50 x^3+16 x^2+65 x+53$
• $y^2=40 x^6+57 x^5+38 x^4+20 x^3+22 x^2+17 x+5$
• $y^2=13 x^6+16 x^5+43 x^4+71 x^3+52 x^2+22 x+2$
• and

• $y^2=39 x^6+64 x^5+53 x^4+69 x^3+51 x^2+57 x+13$
• $y^2=15 x^6+49 x^5+63 x^4+34 x^3+57 x^2+16 x+11$
• $y^2=29 x^6+39 x^5+59 x^4+27 x^3+39 x^2+20 x+10$
• $y^2=15 x^6+4 x^5+68 x^4+70 x^3+46 x^2+9 x+17$
• $y^2=32 x^6+57 x^5+64 x^4+7 x^3+5 x^2+9 x+13$
• $y^2=34 x^6+22 x^5+41 x^4+68 x^3+49 x^2+58 x+44$
• $y^2=51 x^6+8 x^5+57 x^4+23 x^3+57 x^2+8 x+51$
• $y^2=65 x^6+34 x^5+9 x^4+51 x^3+38 x^2+8 x+49$
• $y^2=42 x^6+59 x^5+49 x^4+x^3+15 x^2+64 x+40$
• $y^2=8 x^6+5 x^5+17 x^4+9 x^3+17 x^2+5 x+8$
• $y^2=x^6+16 x^5+32 x^4+68 x^3+68 x^2+10 x+54$
• $y^2=48 x^6+19 x^4+19 x^2+48$
• $y^2=52 x^6+6 x^5+14 x^4+38 x^3+33 x^2+70 x+37$
• $y^2=6 x^6+9 x^5+38 x^4+47 x^3+25 x^2+18 x+54$
• $y^2=37 x^6+3 x^5+33 x^4+25 x^3+71 x^2+19 x+18$
• $y^2=62 x^6+55 x^5+66 x^4+4 x^3+35 x^2+64 x+58$
• $y^2=49 x^6+26 x^5+3 x^4+20 x^3+17 x^2+71 x+68$
• $y^2=54 x^6+4 x^5+x^4+27 x^3+42 x^2+6 x+30$
• $y^2=x^6+2 x^3+8$
• $y^2=26 x^6+57 x^5+49 x^4+8 x^3+24 x^2+50 x+23$
• $y^2=21 x^6+51 x^5+25 x^4+33 x^3+25 x^2+51 x+21$
• $y^2=x^6+38 x^3+49$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{73}$

The isogeny class factors as 1.73.ai^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-57}) \)$)$

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_de	$2$	(not in LMFDB)
2.73.q_ic	$2$	(not in LMFDB)
2.73.i_aj	$3$	(not in LMFDB)