Abelian variety isogeny class 2.83.aq_iw over $\F_{83}$

• Label: 2.83.aq_iw
• Base field: $\F_{83}$
• 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:	$\F_{83}$
Dimension:	$2$
L-polynomial:	$( 1 - 8 x + 83 x^{2} )^{2}$
	$1 - 16 x + 230 x^{2} - 1328 x^{3} + 6889 x^{4}$
Frobenius angles:	$\pm0.355312599736$, $\pm0.355312599736$
Angle rank:	$1$ (numerical)
Jacobians:	$46$
Cyclic group of points:	no
Non-cyclic primes:	$2, 19$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$5776$	$48888064$	$328636199824$	$2252612587196416$	$15515286105935481616$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$68$	$7094$	$574748$	$47465070$	$3938848948$	$326938279718$	$27136050151180$	$2252292399204574$	$186940256673655844$	$15516041184588337814$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 46 curves (of which all are hyperelliptic):

• $y^2=80 x^6+23 x^4+23 x^2+80$
• $y^2=78 x^6+48 x^5+25 x^4+56 x^3+4 x^2+21 x+73$
• $y^2=12 x^6+59 x^5+57 x^4+74 x^3+34 x^2+5 x+77$
• $y^2=40 x^5+78 x^4+75 x^3+28 x^2+44 x+66$
• $y^2=7 x^6+23 x^5+28 x^4+43 x^3+40 x^2+11 x+82$
• $y^2=80 x^6+40 x^5+45 x^4+29 x^3+39 x^2+61 x+12$
• $y^2=23 x^6+70 x^5+38 x^4+7 x^3+24 x^2+35 x+24$
• $y^2=33 x^6+23 x^5+66 x^4+68 x^3+7 x^2+53 x+59$
• $y^2=56 x^6+41 x^5+33 x^4+54 x^3+69 x^2+x+53$
• $y^2=x^6+40 x^5+65 x^4+56 x^3+82 x^2+63 x+43$
• $y^2=19 x^6+40 x^5+21 x^4+44 x^3+x^2+59 x+54$
• $y^2=11 x^5+43 x^4+74 x^3+44 x^2+9 x+63$
• $y^2=18 x^6+31 x^5+58 x^4+5 x^3+31 x^2+37 x+24$
• $y^2=73 x^6+39 x^5+78 x^4+26 x^3+11 x^2+29 x+25$
• $y^2=23 x^6+67 x^4+67 x^2+23$
• $y^2=4 x^6+67 x^5+31 x^4+39 x^3+48 x^2+28 x+56$
• $y^2=x^6+35 x^5+56 x^4+82 x^3+14 x^2+29 x+44$
• $y^2=55 x^6+22 x^5+67 x^4+7 x^3+53 x^2+31 x+17$
• $y^2=45 x^6+38 x^5+25 x^4+44 x^3+52 x^2+65 x+19$
• $y^2=39 x^6+14 x^5+62 x^4+47 x^3+44 x^2+77 x+9$
• and

• $y^2=58 x^6+51 x^5+28 x^4+66 x^3+28 x^2+51 x+58$
• $y^2=6 x^6+41 x^5+45 x^4+37 x^3+46 x^2+2 x+48$
• $y^2=69 x^6+75 x^5+3 x^4+11 x^3+48 x^2+49 x+39$
• $y^2=32 x^6+68 x^5+81 x^4+x^3+34 x^2+6 x+26$
• $y^2=39 x^6+19 x^5+52 x^4+48 x^3+50 x^2+63 x+69$
• $y^2=35 x^6+64 x^5+68 x^4+35 x^3+44 x^2+11 x+74$
• $y^2=29 x^6+30 x^5+50 x^4+43 x^3+54 x^2+28 x+73$
• $y^2=17 x^6+3 x^5+58 x^4+41 x^3+5 x^2+32 x+21$
• $y^2=39 x^6+16 x^5+46 x^4+53 x^3+61 x^2+42 x+20$
• $y^2=20 x^6+78 x^5+21 x^4+35 x^3+51 x^2+x+14$
• $y^2=12 x^6+39 x^4+39 x^2+12$
• $y^2=65 x^6+79 x^5+3 x^4+42 x^3+70 x^2+51 x+24$
• $y^2=66 x^6+75 x^5+52 x^4+67 x^3+34 x^2+18 x+50$
• $y^2=81 x^6+24 x^5+68 x^4+78 x^3+68 x^2+24 x+81$
• $y^2=8 x^6+32 x^5+74 x^4+24 x^3+80 x^2+48 x+48$
• $y^2=51 x^6+82 x^5+23 x^4+56 x^3+40 x^2+58 x+44$
• $y^2=52 x^6+32 x^5+13 x^4+82 x^3+78 x^2+15 x+4$
• $y^2=23 x^6+17 x^5+13 x^4+26 x^3+41 x^2+59 x+2$
• $y^2=74 x^6+19 x^5+82 x^4+49 x^3+33 x^2+27 x+42$
• $y^2=77 x^6+46 x^5+58 x^4+38 x^3+80 x^2+59 x+16$
• $y^2=21 x^6+48 x^5+13 x^4+2 x^3+49 x^2+15 x+55$
• $y^2=50 x^6+45 x^5+26 x^4+53 x^3+26 x^2+45 x+50$
• $y^2=67 x^6+28 x^5+70 x^4+62 x^3+54 x^2+28 x+75$
• $y^2=76 x^6+55 x^5+3 x^4+47 x^3+31 x^2+17 x+20$
• $y^2=20 x^6+70 x^5+8 x^4+4 x^3+39 x^2+15 x+10$
• $y^2=44 x^6+31 x^5+75 x^4+15 x^3+75 x^2+31 x+44$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{83}$.

Endomorphism algebra over $\F_{83}$

The isogeny class factors as 1.83.ai^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-67}) \)$)$

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
2.83.a_dy	$2$	(not in LMFDB)
2.83.q_iw	$2$	(not in LMFDB)
2.83.i_at	$3$	(not in LMFDB)