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

• Label: 2.83.ad_acw
• Base field: $\F_{83}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: yes
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{83}$
Dimension:	$2$
L-polynomial:	$1 - 3 x - 74 x^{2} - 249 x^{3} + 6889 x^{4}$
Frobenius angles:	$\pm0.114018371299$, $\pm0.780685037966$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-3}, \sqrt{-323})\)
Galois group:	$C_2^2$
Jacobians:	$52$
Cyclic group of points:	no
Non-cyclic primes:	$2$

This isogeny class is simple but not geometrically 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$6564$	$46394352$	$326118660624$	$2252808222277824$	$15515677330798175724$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$81$	$6733$	$570348$	$47469193$	$3938948271$	$326941623718$	$27136060532109$	$2252292255401041$	$186940256991164244$	$15516041187860543293$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 52 curves (of which all are hyperelliptic):

• $y^2=68 x^6+80 x^5+43 x^4+17 x^3+3 x^2+82 x+63$
• $y^2=47 x^6+34 x^5+36 x^4+28 x^3+71 x^2+5 x+16$
• $y^2=80 x^6+36 x^5+54 x^4+29 x^3+33 x^2+37 x+37$
• $y^2=51 x^6+57 x^4+40 x^3+49 x^2+7 x+81$
• $y^2=23 x^6+59 x^5+x^4+26 x^3+48 x^2+43 x+27$
• $y^2=4 x^6+21 x^5+4 x^4+67 x^3+35 x^2+25 x+21$
• $y^2=68 x^6+58 x^5+66 x^4+24 x^3+49 x^2+18 x+68$
• $y^2=60 x^6+2 x^5+21 x^4+6 x^3+37 x^2+58 x$
• $y^2=52 x^6+23 x^5+49 x^4+22 x^3+72 x^2+65 x+54$
• $y^2=77 x^6+67 x^5+13 x^4+12 x^3+76 x^2+78 x+9$
• $y^2=3 x^6+23 x^5+33 x^4+68 x^3+33 x^2+53 x+43$
• $y^2=13 x^6+4 x^5+74 x^4+77 x^3+30 x^2+30 x+55$
• $y^2=22 x^6+18 x^5+39 x^4+52 x^3+40 x^2+30 x+37$
• $y^2=42 x^6+54 x^5+31 x^4+46 x^3+59 x^2+32 x+42$
• $y^2=10 x^6+10 x^5+80 x^4+63 x^3+79 x^2+21 x+52$
• $y^2=3 x^6+13 x^5+4 x^4+27 x^3+42 x^2+41 x+41$
• $y^2=45 x^6+34 x^5+54 x^4+67 x^3+69 x^2+54 x+72$
• $y^2=79 x^6+69 x^4+15 x^3+4 x^2+20 x+82$
• $y^2=39 x^6+2 x^5+80 x^4+20 x^3+3 x^2+69 x+20$
• $y^2=4 x^6+34 x^5+52 x^4+55 x^3+61 x^2+61 x+78$
• and

• $y^2=16 x^6+9 x^5+41 x^4+76 x^3+61 x^2+79 x+46$
• $y^2=65 x^6+16 x^5+78 x^4+6 x^3+80 x^2+27 x+49$
• $y^2=68 x^6+x^5+80 x^4+12 x^3+46 x^2+55 x+57$
• $y^2=42 x^6+78 x^5+22 x^4+8 x^3+27 x^2+36 x+74$
• $y^2=14 x^6+72 x^5+81 x^4+25 x^3+14 x^2+12 x+14$
• $y^2=47 x^6+20 x^5+56 x^4+28 x^3+82 x^2+45 x+69$
• $y^2=9 x^6+51 x^5+53 x^4+31 x^3+9 x^2+63 x+17$
• $y^2=24 x^6+5 x^5+47 x^4+29 x^3+41 x^2+52 x+66$
• $y^2=51 x^6+37 x^5+26 x^4+72 x^3+40 x^2+67 x+10$
• $y^2=38 x^6+57 x^5+67 x^4+73 x^3+70 x^2+54 x+9$
• $y^2=41 x^6+63 x^5+48 x^4+75 x^3+57 x^2+57 x+32$
• $y^2=74 x^6+43 x^5+41 x^4+45 x^3+29 x^2+60 x+80$
• $y^2=45 x^6+72 x^5+55 x^4+5 x^3+54 x^2+57 x+10$
• $y^2=6 x^6+67 x^5+33 x^4+50 x^3+40 x^2+67 x+12$
• $y^2=56 x^6+75 x^5+43 x^4+10 x^3+59 x^2+81 x+74$
• $y^2=26 x^6+28 x^5+14 x^4+41 x^3+24 x^2+21 x+34$
• $y^2=72 x^6+13 x^5+59 x^4+15 x^3+25 x^2+40 x+2$
• $y^2=38 x^6+68 x^5+42 x^4+49 x^3+30 x^2+75 x+62$
• $y^2=14 x^6+53 x^5+27 x^4+10 x^3+72 x^2+45 x+38$
• $y^2=46 x^6+18 x^5+22 x^4+64 x^3+65 x^2+34 x+13$
• $y^2=17 x^6+42 x^5+10 x^4+42 x^3+55 x^2+28 x+19$
• $y^2=65 x^6+48 x^5+46 x^4+4 x^3+71 x^2+54 x+40$
• $y^2=2 x^6+10 x^5+9 x^4+27 x^3+9 x^2+31 x+48$
• $y^2=10 x^6+19 x^5+48 x^4+55 x^3+13 x^2+2 x+71$
• $y^2=55 x^6+55 x^5+50 x^4+36 x^3+49 x^2+44 x+71$
• $y^2=46 x^6+46 x^5+65 x^4+39 x^3+60 x^2+30 x+20$
• $y^2=18 x^6+53 x^5+43 x^4+x^3+48 x^2+55 x+18$
• $y^2=71 x^6+68 x^5+21 x^4+48 x^3+21 x^2+59 x+14$
• $y^2=65 x^6+47 x^5+57 x^4+17 x^3+57 x^2+58 x+58$
• $y^2=24 x^6+48 x^5+3 x^4+70 x^3+44 x^2+77 x+66$
• $y^2=41 x^6+24 x^5+62 x^4+11 x^3+25 x^2+4$
• $y^2=13 x^6+32 x^5+6 x^4+4 x^3+49 x^2+9 x+60$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{83^{3}}$.

Endomorphism algebra over $\F_{83}$

The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-3}, \sqrt{-323})\).

Endomorphism algebra over $\overline{\F}_{83}$

The base change of $A$ to $\F_{83^{3}}$ is 1.571787.abbs^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.d_acw	$2$	(not in LMFDB)
2.83.g_gt	$3$	(not in LMFDB)
2.83.ag_gt	$6$	(not in LMFDB)