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

• Label: 2.73.c_fr
• 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:	$( 1 + x + 73 x^{2} )^{2}$
	$1 + 2 x + 147 x^{2} + 146 x^{3} + 5329 x^{4}$
Frobenius angles:	$\pm0.518638325776$, $\pm0.518638325776$
Angle rank:	$1$ (numerical)
Jacobians:	$56$
Cyclic group of points:	no
Non-cyclic primes:	$3, 5$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$5625$	$29975625$	$151165440000$	$805871447015625$	$4297734799329515625$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$76$	$5620$	$388582$	$28377508$	$2073124156$	$151335687310$	$11047393221052$	$806459990537668$	$58871587196381686$	$4297625836614462100$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 56 curves (of which all are hyperelliptic):

• $y^2=62 x^6+42 x^5+34 x^4+53 x^3+59 x^2+44 x+62$
• $y^2=17 x^6+46 x^5+45 x^4+68 x^3+61 x^2+66 x+6$
• $y^2=3 x^6+19 x^5+70 x^4+66 x^3+27 x^2+6 x+3$
• $y^2=3 x^6+49 x^5+18 x^4+58 x^3+39 x^2+50 x+31$
• $y^2=64 x^6+42 x^5+10 x^4+50 x^3+14 x^2+59 x+34$
• $y^2=5 x^6+41 x^5+53 x^4+41 x^3+44 x^2+32 x+11$
• $y^2=10 x^6+13 x^5+64 x^4+29 x^3+63 x^2+24 x+11$
• $y^2=34 x^6+58 x^5+16 x^4+68 x^3+18 x^2+3 x+32$
• $y^2=14 x^6+46 x^5+72 x^4+37 x^3+53 x^2+20 x+36$
• $y^2=44 x^6+71 x^5+50 x^4+29 x^3+50 x^2+50$
• $y^2=10 x^6+60 x^5+27 x^4+44 x^3+61 x^2+19 x+72$
• $y^2=5 x^6+67 x^5+12 x^4+57 x^3+69 x^2+48 x+62$
• $y^2=38 x^6+28 x^5+43 x^4+69 x^3+46 x^2+32 x+27$
• $y^2=28 x^6+9 x^5+70 x^4+64 x^3+50 x^2+18 x+40$
• $y^2=6 x^6+43 x^5+55 x^4+67 x^3+36 x^2+26 x+25$
• $y^2=39 x^6+17 x^5+55 x^4+24 x^3+23 x^2+27 x+67$
• $y^2=68 x^6+25 x^5+69 x^4+31 x^3+15 x^2+71 x+61$
• $y^2=34 x^6+30 x^5+37 x^4+6 x^3+35 x^2+51 x+31$
• $y^2=12 x^6+21 x^5+69 x^4+35 x^3+59 x^2+12 x+7$
• $y^2=56 x^6+31 x^5+16 x^4+38 x^3+2 x^2+29 x+56$
• and

• $y^2=37 x^6+18 x^5+64 x^4+24 x^3+9 x^2+18 x+36$
• $y^2=65 x^6+59 x^5+22 x^4+41 x^3+x^2+50 x+64$
• $y^2=20 x^6+64 x^5+48 x^4+55 x^3+28 x^2+43 x+47$
• $y^2=62 x^6+37 x^5+62 x^4+54 x^3+58 x^2+32 x+62$
• $y^2=62 x^6+27 x^5+46 x^4+48 x^3+19 x^2+35 x+58$
• $y^2=72 x^6+45 x^5+6 x^4+29 x^3+2 x^2+5 x+27$
• $y^2=43 x^6+18 x^5+68 x^4+61 x^3+49 x^2+10 x+8$
• $y^2=36 x^6+19 x^5+6 x^4+5 x^3+48 x^2+44 x+39$
• $y^2=63 x^6+22 x^5+69 x^4+20 x^3+69 x^2+7 x+36$
• $y^2=52 x^6+54 x^5+41 x^4+12 x^3+36 x^2+24 x+63$
• $y^2=23 x^6+56 x^5+4 x^4+29 x^3+64 x^2+28 x+38$
• $y^2=36 x^6+33 x^5+64 x^4+18 x^3+70 x^2+28 x+50$
• $y^2=49 x^6+49 x^5+40 x^4+14 x^3+18 x^2+61 x+47$
• $y^2=34 x^6+43 x^5+45 x^4+30 x^3+44 x^2+60 x+13$
• $y^2=59 x^6+22 x^5+28 x^4+27 x^3+6 x^2+67 x+44$
• $y^2=54 x^6+46 x^5+26 x^4+65 x^3+34 x^2+67 x+55$
• $y^2=38 x^6+11 x^5+25 x^4+25 x^3+15 x^2+8 x+55$
• $y^2=9 x^6+20 x^5+69 x^4+29 x^3+4 x^2+20 x+64$
• $y^2=71 x^6+58 x^5+59 x^4+3 x^3+2 x^2+9 x+30$
• $y^2=51 x^6+16 x^5+30 x^4+28 x^3+47 x^2+54 x+63$
• $y^2=38 x^6+32 x^5+24 x^4+48 x^3+62 x^2+53 x+8$
• $y^2=35 x^6+54 x^5+40 x^4+61 x^3+30 x^2+68 x+65$
• $y^2=7 x^6+34 x^5+37 x^4+8 x^3+56 x^2+5 x+59$
• $y^2=18 x^6+60 x^5+3 x^4+8 x^3+48 x^2+38 x+57$
• $y^2=25 x^6+19 x^5+33 x^4+2 x^3+44 x^2+34 x+21$
• $y^2=68 x^6+37 x^5+12 x^4+19 x^3+62 x^2+51 x+23$
• $y^2=32 x^6+43 x^5+16 x^4+37 x^3+64 x^2+31 x+4$
• $y^2=48 x^6+3 x^5+14 x^4+63 x^3+5 x^2+13 x+5$
• $y^2=x^6+18 x^3+65$
• $y^2=x^6+32 x^3+64$
• $y^2=14 x^6+3 x^5+53 x^4+45 x^3+52 x^2+67 x+29$
• $y^2=44 x^6+61 x^5+15 x^4+10 x^3+29 x^2+70 x+31$
• $y^2=50 x^6+37 x^5+7 x^4+51 x^3+26 x^2+35 x+28$
• $y^2=49 x^6+35 x^5+38 x^4+41 x^3+21 x^2+27 x+63$
• $y^2=59 x^6+70 x^5+16 x^4+71 x^3+3 x^2+19 x+70$
• $y^2=52 x^6+21 x^5+4 x^4+59 x^3+41 x^2+18 x+11$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{73}$

The isogeny class factors as 1.73.b^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-291}) \)$)$

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.ac_fr	$2$	(not in LMFDB)
2.73.a_fp	$2$	(not in LMFDB)
2.73.ab_acu	$3$	(not in LMFDB)