Abelian variety isogeny class 3.19.aj_cl_aml over $\F_{19}$

• Label: 3.19.aj_cl_aml
• Base field: $\F_{19}$
• Dimension: $3$
• $p$-rank: $2$
• Ordinary: no
• Supersingular: no
• Simple: yes
• Geometrically simple: yes
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{19}$
Dimension:	$3$
L-polynomial:	$1 - 9 x + 63 x^{2} - 323 x^{3} + 1197 x^{4} - 3249 x^{5} + 6859 x^{6}$
Frobenius angles:	$\pm0.135165518629$, $\pm0.420208233711$, $\pm0.540494570088$
Angle rank:	$3$ (numerical)
Number field:	6.0.451390239.2
Galois group:	$A_4\times C_2$
Cyclic group of points:	yes

This isogeny class is simple and geometrically simple, primitive, not ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

$p$-rank:	$2$
Slopes:	$[0, 0, 1/2, 1/2, 1, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$4539$	$53110839$	$322905381417$	$2197641593588439$	$15184382590865152029$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$11$	$407$	$6863$	$129395$	$2476631$	$47068079$	$893942984$	$16983788051$	$322688736113$	$6131065952747$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 20 hyperelliptic curves, but it is unknown how many Jacobians of non-hyperelliptic curves it contains:

• $y^2=18 x^7+9 x^5+6 x^4+15 x^3+16 x^2+14 x+10$
• $y^2=x^7+11 x^5+5 x^4+13 x^3+10 x^2+3 x+8$
• $y^2=18 x^7+11 x^4+14 x^3+4 x^2+18$
• $y^2=18 x^7+18 x^5+2 x^4+10 x^3+15 x^2+17 x+3$
• $y^2=x^7+17 x^5+18 x^4+6 x^3+8 x^2+14 x+3$
• $y^2=18 x^7+13 x^5+14 x^4+6 x^3+2 x^2+5 x+13$
• $y^2=x^7+15 x^5+18 x^4+18 x^3+15 x^2+10 x+2$
• $y^2=18 x^7+15 x^5+17 x^4+14 x^3+14 x^2+6 x+2$
• $y^2=18 x^7+13 x^5+10 x^4+4 x^3+3 x^2+8 x+13$
• $y^2=18 x^7+17 x^5+15 x^4+7 x^3+11 x^2+7 x+6$
• $y^2=x^7+13 x^5+17 x^4+5 x^3+6 x^2+14$
• $y^2=x^7+17 x^5+8 x^4+12 x^3+5 x^2+12 x+12$
• $y^2=18 x^7+10 x^5+13 x^4+5 x^3+10 x^2+x+8$
• $y^2=18 x^7+2 x^5+18 x^4+16 x^3+4 x^2+5 x+12$
• $y^2=x^7+12 x^5+16 x^4+5 x^3+13 x^2+14 x+8$
• $y^2=18 x^7+14 x^5+7 x^4+12 x^3+17 x^2+13 x+13$
• $y^2=18 x^7+x^5+5 x^4+14 x^3+6 x^2+15 x+12$
• $y^2=18 x^7+15 x^5+x^3+7 x^2+18 x+12$
• $y^2=x^7+14 x^5+12 x^4+2 x^3+9 x^2+14 x+17$
• $y^2=x^7+3 x^5+15 x^4+x^3+16 x^2+6$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{19}$.

Endomorphism algebra over $\F_{19}$

The endomorphism algebra of this simple isogeny class is 6.0.451390239.2.

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
3.19.j_cl_ml	$2$	(not in LMFDB)