Abelian variety isogeny class 2.41.as_fw over $\F_{41}$

• Label: 2.41.as_fw
• Base field: $\F_{41}$
• 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:	$\F_{41}$
Dimension:	$2$
L-polynomial:	$1 - 18 x + 152 x^{2} - 738 x^{3} + 1681 x^{4}$
Frobenius angles:	$\pm0.0883036955963$, $\pm0.353631113310$
Angle rank:	$2$ (numerical)
Number field:	4.0.38720.3
Galois group:	$D_{4}$
Jacobians:	$22$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$1078$	$2792020$	$4761225238$	$7983222786000$	$13420342712719558$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$24$	$1662$	$69084$	$2825158$	$115836204$	$4749989262$	$194754525864$	$7984933498558$	$327381993703944$	$13422659500021902$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 22 curves (of which all are hyperelliptic):

• $y^2=30 x^6+16 x^5+19 x^4+32 x^3+12 x^2+6 x+14$
• $y^2=17 x^6+6 x^5+18 x^4+32 x^3+39 x^2+12 x+16$
• $y^2=24 x^6+6 x^5+8 x^4+16 x^3+10 x^2+27 x+20$
• $y^2=30 x^6+15 x^5+9 x^4+23 x^3+18 x^2+27 x+19$
• $y^2=24 x^6+34 x^5+31 x^4+24 x^3+33 x^2+5 x+16$
• $y^2=2 x^6+40 x^5+x^4+33 x^3+39 x^2+7 x+15$
• $y^2=24 x^6+12 x^5+18 x^4+28 x^3+4 x^2+17 x+2$
• $y^2=24 x^6+36 x^5+32 x^4+9 x^3+36 x^2+38 x+27$
• $y^2=35 x^6+22 x^5+28 x^4+22 x^3+17 x^2+29 x+15$
• $y^2=11 x^6+15 x^5+22 x^4+35 x^3+16 x^2+33 x+28$
• $y^2=19 x^6+35 x^5+17 x^4+27 x^3+13 x^2+20 x+14$
• $y^2=11 x^6+18 x^5+40 x^4+11 x^3+10 x^2+8 x+10$
• $y^2=27 x^6+5 x^5+37 x^4+5 x^3+7 x^2+2 x+34$
• $y^2=34 x^6+21 x^5+33 x^4+27 x^3+19 x^2+18 x+36$
• $y^2=10 x^6+3 x^5+34 x^4+19 x^3+28 x^2+37 x+17$
• $y^2=14 x^6+21 x^5+8 x^4+36 x^3+30 x^2+30 x$
• $y^2=9 x^5+35 x^4+35 x^3+17 x^2+27 x+34$
• $y^2=21 x^6+9 x^5+15 x^4+11 x^3+10 x^2+14 x+13$
• $y^2=23 x^6+39 x^5+29 x^4+19 x^3+36 x^2+12 x+29$
• $y^2=28 x^6+27 x^5+8 x^4+38 x^3+20 x^2+2 x+3$
• $y^2=10 x^6+39 x^5+16 x^4+6 x^3+33 x^2+27 x+24$
• $y^2=30 x^6+27 x^5+10 x^4+28 x^3+34 x^2+29 x+13$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{41}$.

Endomorphism algebra over $\F_{41}$

The endomorphism algebra of this simple isogeny class is 4.0.38720.3.

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
2.41.s_fw	$2$	(not in LMFDB)