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

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

Invariants

Base field:	$\F_{83}$
Dimension:	$2$
L-polynomial:	$1 - 29 x + 365 x^{2} - 2407 x^{3} + 6889 x^{4}$
Frobenius angles:	$\pm0.0639743454557$, $\pm0.290481692689$
Angle rank:	$2$ (numerical)
Number field:	4.0.68725.1
Galois group:	$D_{4}$
Jacobians:	$15$

This isogeny class is simple and 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$4819$	$46700929$	$327022693909$	$2252409576442861$	$15515849740694096464$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$55$	$6779$	$571933$	$47460795$	$3938992040$	$326939174903$	$27136038928151$	$2252292185770339$	$186940255775410009$	$15516041198082912614$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 15 curves (of which all are hyperelliptic):

• $y^2=80 x^6+25 x^5+68 x^4+65 x^3+9 x^2+13 x+51$
• $y^2=15 x^6+82 x^5+31 x^4+59 x^3+45 x^2+7 x+81$
• $y^2=79 x^6+43 x^5+35 x^4+29 x^3+28 x^2+60 x+46$
• $y^2=32 x^6+25 x^5+42 x^4+26 x^3+54 x^2+44 x+74$
• $y^2=64 x^6+28 x^5+16 x^4+63 x^3+62 x^2+53 x+10$
• $y^2=64 x^6+56 x^5+46 x^4+x^3+19 x^2+12 x+70$
• $y^2=x^6+78 x^5+46 x^4+36 x^2+11 x+48$
• $y^2=71 x^6+20 x^5+71 x^4+41 x^3+49 x^2+35 x+15$
• $y^2=75 x^6+55 x^5+13 x^4+57 x^3+8 x^2+7 x+79$
• $y^2=72 x^6+13 x^5+11 x^4+82 x^3+66 x^2+57 x+5$
• $y^2=66 x^6+26 x^5+80 x^4+17 x^3+49 x^2+40 x+60$
• $y^2=82 x^6+44 x^5+20 x^4+80 x^3+74 x^2+35 x+3$
• $y^2=45 x^6+4 x^5+72 x^4+55 x^3+9 x^2+73 x+68$
• $y^2=5 x^6+28 x^5+76 x^4+43 x^3+5 x^2+73 x+71$
• $y^2=22 x^6+28 x^5+38 x^4+79 x^3+50 x^2+35 x+46$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{83}$

The endomorphism algebra of this simple isogeny class is 4.0.68725.1.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.

Twist	Extension degree	Common base change
2.83.bd_ob	$2$	(not in LMFDB)