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

• Label: 2.83.g_gt
• 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:	$( 1 + 3 x + 83 x^{2} )^{2}$
	$1 + 6 x + 175 x^{2} + 498 x^{3} + 6889 x^{4}$
Frobenius angles:	$\pm0.552648295368$, $\pm0.552648295368$
Angle rank:	$1$ (numerical)
Jacobians:	$62$
Cyclic group of points:	no
Non-cyclic primes:	$3, 29$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$7569$	$49660209$	$326118660624$	$2251260606397401$	$15516768925619522289$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$90$	$7204$	$570348$	$47436580$	$3939225390$	$326941623718$	$27136031904666$	$2252292185615044$	$186940256991164244$	$15516041185896473764$

Jacobians and polarizations

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

• $y^2=40 x^6+42 x^5+31 x^4+75 x^3+36 x^2+61 x+35$
• $y^2=8 x^6+17 x^5+16 x^4+3 x^3+75 x^2+61 x+16$
• $y^2=41 x^6+37 x^5+75 x^4+33 x^3+75 x^2+37 x+41$
• $y^2=58 x^6+71 x^5+29 x^4+21 x^3+29 x^2+68 x+14$
• $y^2=10 x^6+22 x^4+44 x^3+22 x^2+10$
• $y^2=75 x^6+44 x^5+38 x^4+38 x^3+38 x^2+44 x+75$
• $y^2=75 x^6+65 x^5+73 x^4+64 x^3+73 x^2+65 x+75$
• $y^2=52 x^6+7 x^5+29 x^4+79 x^3+29 x^2+7 x+52$
• $y^2=37 x^6+10 x^5+42 x^4+56 x^3+60 x^2+78 x+21$
• $y^2=66 x^6+10 x^5+82 x^4+19 x^3+40 x^2+38 x+68$
• $y^2=62 x^6+46 x^5+70 x^4+32 x^3+69 x^2+69 x+81$
• $y^2=78 x^6+12 x^5+x^4+2 x^3+66 x^2+75 x+64$
• $y^2=26 x^6+63 x^5+28 x^4+48 x^3+55 x^2+75 x+59$
• $y^2=50 x^6+79 x^5+57 x^4+28 x^3+23 x^2+75 x+61$
• $y^2=11 x^6+37 x^5+48 x^4+76 x^3+45 x^2+56 x+36$
• $y^2=82 x^6+80 x^5+23 x^4+71 x^3+23 x^2+80 x+82$
• $y^2=7 x^6+47 x^5+32 x^4+43 x^3+50 x^2+82 x+48$
• $y^2=46 x^6+43 x^5+37 x^4+62 x^3+37 x^2+43 x+46$
• $y^2=69 x^6+60 x^5+39 x^4+42 x^3+26 x^2+69 x+73$
• $y^2=11 x^6+43 x^5+58 x^4+x^3+43 x^2+41 x+43$
• and

• $y^2=52 x^6+x^5+80 x^4+30 x^3+14 x^2+78 x+21$
• $y^2=82 x^6+78 x^5+24 x^4+27 x^3+3 x^2+3 x+81$
• $y^2=38 x^6+15 x^5+31 x^4+81 x^3+x^2+11 x+35$
• $y^2=45 x^6+78 x^5+26 x^4+20 x^3+42 x^2+56 x+80$
• $y^2=73 x^6+81 x^5+60 x^4+66 x^3+60 x^2+81 x+73$
• $y^2=50 x^6+75 x^5+x^4+73 x^3+47 x^2+23$
• $y^2=65 x^6+3 x^5+30 x^4+29 x^3+30 x^2+3 x+65$
• $y^2=46 x^6+11 x^5+54 x^4+63 x^3+45 x^2+80 x+28$
• $y^2=15 x^6+66 x^5+22 x^4+14 x^3+22 x^2+66 x+15$
• $y^2=8 x^6+45 x^5+72 x^4+5 x^3+53 x^2+13 x+39$
• $y^2=70 x^6+44 x^5+71 x^4+70 x^3+75 x^2+33 x+20$
• $y^2=44 x^6+16 x^5+42 x^4+77 x^3+33 x^2+36 x+20$
• $y^2=45 x^6+4 x^5+30 x^4+59 x^3+55 x^2+9 x+1$
• $y^2=28 x^6+34 x^5+69 x^4+9 x^3+79 x^2+16 x+70$
• $y^2=35 x^6+28 x^5+7 x^4+35 x^3+58 x^2+11 x+23$
• $y^2=12 x^6+16 x^5+21 x^4+64 x^3+19 x^2+41 x+29$
• $y^2=63 x^6+13 x^5+39 x^4+x^3+45 x^2+45 x+39$
• $y^2=7 x^6+8 x^5+66 x^4+38 x^3+66 x^2+8 x+7$
• $y^2=12 x^6+54 x^5+59 x^4+75 x^3+27 x^2+81 x+67$
• $y^2=64 x^6+20 x^5+39 x^4+44 x^3+39 x^2+20 x+64$
• $y^2=x^6+31 x^5+20 x^4+64 x^3+41 x^2+17 x+41$
• $y^2=31 x^6+44 x^5+57 x^4+36 x^3+57 x^2+44 x+31$
• $y^2=77 x^6+25 x^5+32 x^4+79 x^3+25 x^2+13 x+19$
• $y^2=70 x^6+54 x^5+8 x^4+70 x^3+8 x^2+54 x+70$
• $y^2=15 x^6+17 x^5+72 x^4+52 x^3+42 x^2+24 x+5$
• $y^2=43 x^6+22 x^5+80 x^4+41 x^3+57 x^2+30 x+62$
• $y^2=13 x^6+17 x^5+72 x^4+21 x^3+20 x^2+41 x+80$
• $y^2=40 x^6+46 x^5+38 x^4+48 x^3+35 x^2+23 x+31$
• $y^2=60 x^6+40 x^5+3 x^4+41 x^3+3 x^2+40 x+60$
• $y^2=75 x^6+56 x^5+18 x^4+4 x^3+18 x^2+56 x+75$
• $y^2=28 x^6+56 x^5+41 x^4+64 x^3+27 x^2+37 x+59$
• $y^2=19 x^6+53 x^5+56 x^4+28 x^3+8 x^2+34 x+19$
• $y^2=39 x^6+2 x^5+55 x^4+17 x^3+62 x^2+9 x+7$
• $y^2=55 x^6+25 x^5+74 x^4+46 x^3+x^2+32 x+41$
• $y^2=2 x^6+28 x^5+2 x^4+38 x^3+62 x^2+16 x+71$
• $y^2=31 x^6+71 x^5+43 x^4+59 x^3+20 x^2+58 x+5$
• $y^2=74 x^6+77 x^5+62 x^4+33 x^3+74 x^2+54 x+36$
• $y^2=23 x^6+61 x^5+34 x^4+31 x^3+34 x^2+61 x+23$
• $y^2=10 x^6+37 x^5+17 x^4+13 x^3+24 x^2+51 x+7$
• $y^2=81 x^6+6 x^5+x^4+5 x^3+x^2+6 x+81$
• $y^2=3 x^6+6 x^5+5 x^4+37 x^3+53 x^2+56 x+80$
• $y^2=39 x^6+9 x^5+37 x^4+13 x^3+61 x^2+62 x+23$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{83}$

The isogeny class factors as 1.83.d^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-323}) \)$)$

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.ag_gt	$2$	(not in LMFDB)
2.83.a_gb	$2$	(not in LMFDB)
2.83.ad_acw	$3$	(not in LMFDB)