Abelian variety isogeny class 3.13.c_l_ae over $\F_{13}$

• Label: 3.13.c_l_ae
• Base field: $\F_{13}$
• Dimension: $3$
• $p$-rank: $3$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{13}$
Dimension:	$3$
L-polynomial:	$( 1 + 2 x + 13 x^{2} )( 1 - 2 x^{2} + 169 x^{4} )$
	$1 + 2 x + 11 x^{2} - 4 x^{3} + 143 x^{4} + 338 x^{5} + 2197 x^{6}$
Frobenius angles:	$\pm0.237745206151$, $\pm0.589456187511$, $\pm0.762254793849$
Angle rank:	$2$ (numerical)

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:	$3$
Slopes:	$[0, 0, 0, 1, 1, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$2688$	$5419008$	$10273592448$	$23726758035456$	$51351632897728128$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$16$	$188$	$2128$	$29084$	$372496$	$4828316$	$62733904$	$815657660$	$10604617744$	$137857231868$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 285 hyperelliptic curves, but it is unknown how many Jacobians of non-hyperelliptic curves it contains:

• $y^2=2 x^7+8 x^6+2 x^5+12 x^4+8 x^3+8 x^2+12 x$
• $y^2=2 x^7+8 x^6+8 x^5+6 x^4+9 x^3+9 x^2+10 x$
• $y^2=x^7+x^6+10 x^5+6 x^4+5 x^3+11 x^2+5 x$
• $y^2=2 x^7+8 x^6+x^3+2 x$
• $y^2=2 x^7+10 x^6+3 x^5+8 x^4+11 x^3+2 x^2+3 x$
• $y^2=x^7+x^6+7 x^5+5 x^4+x^3+7 x^2+4 x$
• $y^2=x^7+6 x^6+3 x^5+x^4+x^3+3 x^2+6 x+1$
• $y^2=x^7+2 x^6+7 x^5+4 x^3+4 x^2+6$
• $y^2=2 x^7+2 x^6+4 x^5+2 x^4+10 x^3+8 x^2+8 x$
• $y^2=2 x^7+6 x^6+6 x^5+6 x^4+12 x^3+11 x^2+3 x$
• $y^2=2 x^7+12 x^6+4 x^5+11 x^4+10 x^3+8 x^2+8 x+9$
• $y^2=2 x^7+4 x^6+8 x^5+x^4+x^3+11 x+1$
• $y^2=x^7+2 x^6+9 x^5+7 x^4+9 x^3+11 x^2+11 x+4$
• $y^2=2 x^8+10 x^7+8 x^6+7 x^5+10 x^4+10 x^3+9 x^2+12 x+10$
• $y^2=x^8+2 x^7+x^6+6 x^5+9 x^4+4 x^3+6 x^2+7 x+6$
• $y^2=x^8+3 x^7+10 x^6+2 x^5+3 x^4+4 x^3+x^2+11 x+3$
• $y^2=2 x^8+4 x^7+7 x^6+6 x^5+2 x^4+5 x^3+3 x+3$
• $y^2=2 x^8+10 x^7+9 x^6+4 x^5+10 x^4+8 x^3+10 x^2+2 x+6$
• $y^2=2 x^8+10 x^7+7 x^6+x^5+10 x^4+5 x^3+x^2+x+9$
• $y^2=x^8+3 x^7+x^6+8 x^5+x^4+9 x^3+x^2+9 x+12$
• and

• $y^2=2 x^7+8 x^6+4 x^4+4 x^3+10 x^2+3 x+3$
• $y^2=2 x^8+7 x^6+x^4+2 x^2+1$
• $y^2=2 x^8+4 x^7+12 x^6+9 x^5+x^4+x^3+12 x^2+2 x+2$
• $y^2=2 x^8+8 x^6+x^4+4 x^2+10$
• $y^2=x^8+12 x^7+11 x^6+8 x^5+2 x^4+5 x^3+x+10$
• $y^2=x^8+5 x^7+10 x^6+5 x^5+3 x^4+11 x^3+2 x^2+x+4$
• $y^2=2 x^8+8 x^7+5 x^6+9 x^5+2 x^4+7 x^3+3 x^2+4 x+3$
• $y^2=2 x^8+3 x^7+8 x^5+6 x^4+4 x^3+5 x^2+7 x$
• $y^2=2 x^8+x^7+9 x^6+7 x^5+5 x^4+10 x^3+5 x^2+11 x+12$
• $y^2=x^7+10 x^6+2 x^5+3 x^4+5 x^3+7 x^2+4 x+11$
• $y^2=x^8+9 x^7+8 x^6+x^5+11 x^4+2 x^3+2 x^2+7 x$
• $y^2=x^8+7 x^5+3 x^4+7 x^3+9 x^2+2 x$
• $y^2=2 x^8+9 x^7+8 x^6+4 x^5+10 x^4+5 x^3+7 x^2+6 x+10$
• $y^2=2 x^8+7 x^7+4 x^6+5 x^5+x^4+12 x^2+5 x+3$
• $y^2=x^8+12 x^7+5 x^6+10 x^5+3 x^4+7 x^3+11 x^2+5 x+6$
• $y^2=x^8+9 x^7+5 x^6+3 x^5+7 x^4+4 x^3+2 x^2+2 x+9$
• $y^2=x^8+6 x^6+9 x^5+12 x^4+9 x^3+10 x^2+10 x+12$
• $y^2=2 x^8+11 x^7+5 x^6+10 x^5+9 x^4+4 x^3+10 x^2+9 x+5$
• $y^2=x^8+4 x^7+2 x^6+x^5+9 x^4+8 x^2+x+3$
• $y^2=2 x^8+9 x^7+9 x^6+12 x^5+5 x^4+5 x^2+12 x+12$
• $y^2=2 x^8+4 x^7+12 x^6+2 x^5+11 x^4+x^3+7 x^2+5 x+11$
• $y^2=x^8+2 x^7+x^6+2 x^5+x^4+2 x^3+2 x^2+4 x$
• $y^2=x^8+3 x^7+12 x^6+3 x^5+12 x^4+3 x^3+6 x+9$
• $y^2=2 x^8+12 x^6+4 x^4+10 x^2+3$
• $y^2=x^8+x^7+2 x^6+8 x^5+10 x^4+6 x^3+10 x^2+7 x+10$
• $y^2=2 x^8+5 x^7+4 x^6+7 x^5+5 x^4+9 x^3+x^2+7 x+12$
• $y^2=x^7+11 x^6+5 x^5+10 x^4+10 x^3+x^2+8 x+12$
• $y^2=2 x^7+x^6+x^5+12 x^4+6 x^3+5 x^2+6 x+10$
• $y^2=x^8+7 x^6+3 x^4+4 x^2+11$
• $y^2=2 x^8+11 x^7+11 x^6+4 x^5+7 x^4+12 x^3+10 x^2+7$
• $y^2=x^8+2 x^7+11 x^6+11 x^5+3 x^4+4 x^3+3 x^2+10 x+8$
• $y^2=2 x^8+2 x^7+9 x^6+11 x^5+6 x^4+4 x^3+6 x^2+10 x+3$
• $y^2=x^8+4 x^6+8 x^4+4$
• $y^2=x^8+5 x^7+7 x^6+8 x^5+x^4+10 x^3+2 x^2+12 x+3$
• $y^2=x^8+x^7+9 x^6+8 x^4+3 x^3+2 x^2+9 x+10$
• $y^2=x^8+2 x^7+9 x^6+12 x^5+11 x^4+5 x^3+5 x^2+x+9$
• $y^2=x^8+7 x^6+11 x^4+12 x^2+4$
• $y^2=2 x^8+2 x^7+8 x^6+5 x^5+6 x^4+5 x^3+10 x^2+9 x+7$
• $y^2=2 x^8+2 x^7+3 x^6+11 x^5+10 x^3+4 x^2+7 x+4$
• $y^2=x^8+6 x^5+9 x^4+10 x^3+11 x^2+6 x+5$
• $y^2=2 x^8+2 x^7+10 x^6+8 x^5+4 x^4+4 x^3+4 x^2+9 x+1$
• $y^2=x^8+11 x^6+4 x^5+11 x^4+11 x^3+2 x^2+4 x+6$
• $y^2=x^8+x^7+2 x^6+12 x^5+x^4+11 x^3+10 x^2+6 x+11$
• $y^2=x^8+11 x^6+2 x^4+10$
• $y^2=x^8+8 x^6+4 x^5+2 x^4+7 x^3+11 x^2+4 x+12$
• $y^2=2 x^8+2 x^7+7 x^6+4 x^5+3 x^4+11 x^3+12 x^2+7 x+3$
• $y^2=x^8+6 x^6+5 x^4+9 x^2+12$
• $y^2=2 x^7+10 x^6+8 x^5+11 x^4+6 x^2+2 x$
• $y^2=x^7+3 x^6+11 x^5+x^4+9 x^3+6 x^2+10 x+11$
• $y^2=2 x^7+2 x^6+10 x^5+7 x^4+4 x^2+12 x+1$
• $y^2=2 x^7+4 x^6+10 x^5+8 x^4+10 x^3+7 x+10$
• $y^2=2 x^7+4 x^6+x^5+8 x^4+2 x^3+5 x^2+9 x+10$
• $y^2=x^7+9 x^6+5 x^5+4 x^4+12 x^3+11 x^2+2 x+11$
• $y^2=2 x^7+12 x^6+11 x^5+4 x^4+8 x^3+2 x^2+2 x+12$
• $y^2=x^8+9 x^7+12 x^6+7 x^5+2 x^3+7 x+1$
• $y^2=x^8+10 x^7+5 x^6+3 x^5+3 x^4+x^3+3 x^2+11 x+2$
• $y^2=x^8+11 x^7+3 x^6+12 x^5+8 x^4+7 x^3+9 x^2+12 x+2$
• $y^2=x^8+3 x^7+9 x^6+x^5+10 x^4+x^3+8 x^2+4 x+2$
• $y^2=x^8+9 x^7+6 x^6+2 x^5+7 x^4+11 x^3+11 x^2+11 x+10$
• $y^2=2 x^8+9 x^6+7 x^5+10 x^4+11 x^3+6 x^2+12 x+4$
• $y^2=x^8+x^7+9 x^6+8 x^5+7 x^4+3 x^3+10 x^2+8 x+3$
• $y^2=2 x^8+9 x^7+5 x^6+6 x^5+12 x^4+5 x^2+7 x+2$
• $y^2=x^8+4 x^6+x^5+10 x^4+9 x^3+8 x^2+11 x+3$
• $y^2=x^8+10 x^7+11 x^5+9 x^3+2 x+3$
• $y^2=x^8+6 x^7+6 x^6+5 x^5+10 x^4+6 x^3+11 x^2+3 x+12$
• $y^2=2 x^8+2 x^7+6 x^6+5 x^5+9 x^4+10 x^3+11 x+11$
• $y^2=2 x^8+3 x^7+7 x^4+4 x^3+4 x^2+11 x+1$
• $y^2=2 x^8+12 x^7+8 x^6+4 x^5+8 x^4+5 x^3+11 x^2+10 x+4$
• $y^2=2 x^8+10 x^7+4 x^6+12 x^5+11 x^4+11 x^3+8 x^2+11 x+3$
• $y^2=x^8+4 x^7+8 x^6+3 x^5+6 x^4+7 x^3+6 x^2+11 x+3$
• $y^2=2 x^8+9 x^6+10 x^5+2 x^4+2 x^3+9 x^2+7 x$
• $y^2=x^8+5 x^7+9 x^6+x^5+8 x^3+3 x^2+6 x+9$
• $y^2=x^8+8 x^7+9 x^6+2 x^5+8 x^4+2 x^3+10 x^2+6 x+7$
• $y^2=x^8+5 x^7+x^5+2 x^4+2 x^3+7 x^2+9 x+12$
• $y^2=x^8+5 x^6+4 x^4+x^3+9 x^2+7 x+4$
• $y^2=2 x^8+11 x^7+9 x^6+9 x^5+6 x^4+6 x^3+5 x^2+9 x+11$
• $y^2=2 x^8+6 x^7+8 x^6+9 x^5+12 x^4+3 x^3+11 x^2+9 x+10$
• $y^2=2 x^8+9 x^7+8 x^6+x^5+4 x^4+3 x^3+6 x^2+8 x+10$
• $y^2=2 x^8+x^7+6 x^6+2 x^5+2 x^4+7 x^3+12 x^2+x+10$
• $y^2=x^8+10 x^6+10 x^5+9 x^4+6 x^3+x^2+12 x+12$
• $y^2=x^8+3 x^7+2 x^6+x^5+6 x^4+8 x^3+7 x^2+x+9$
• $y^2=2 x^7+2 x^6+4 x^5+6 x^4+9 x^3+11 x^2+6$
• $y^2=x^8+6 x^7+6 x^6+5 x^5+x^4+9 x^3+5 x^2+5 x+11$
• $y^2=x^8+3 x^7+12 x^6+4 x^5+8 x^4+5 x^3+5 x^2+1$
• $y^2=x^8+12 x^7+6 x^6+12 x^5+4 x^4+4 x^3+8 x^2+x+7$
• $y^2=2 x^8+12 x^7+4 x^6+11 x^5+x^4+6 x^3+12 x^2+3 x+5$
• $y^2=2 x^8+x^7+5 x^6+12 x^5+2 x^4+3 x^2+x$
• $y^2=x^8+6 x^7+5 x^6+5 x^5+12 x^4+4 x^3+11 x^2+2$
• $y^2=x^7+10 x^6+2 x^5+12 x^4+5 x^3+9 x^2+3 x+11$
• $y^2=2 x^8+5 x^7+2 x^6+11 x^5+6 x^4+10 x^3+3 x^2+9 x+4$
• $y^2=x^8+11 x^6+11 x^5+11 x^4+3 x^3+6 x^2+9 x+11$
• $y^2=2 x^8+6 x^7+5 x^6+5 x^5+12 x^4+2 x^2+12 x+9$
• $y^2=2 x^7+2 x^6+6 x^5+4 x^4+x^3+2 x^2+8 x+10$
• $y^2=2 x^8+x^7+3 x^6+12 x^5+10 x^4+2 x^3+9 x^2+3 x+12$
• $y^2=x^7+10 x^6+11 x^5+2 x^4+9 x^3+8 x^2+5 x+5$
• $y^2=x^8+4 x^7+7 x^6+10 x^5+10 x^4+8 x^3+10 x^2+x+1$
• $y^2=2 x^8+5 x^6+2 x^5+8 x^4+12 x^3+4 x^2+11 x+9$
• $y^2=2 x^8+6 x^6+3 x^5+10 x^4+4 x^3+8 x^2+6 x+3$
• $y^2=2 x^8+11 x^7+8 x^6+2 x^5+3 x^4+x^3+6 x^2+2 x$
• $y^2=2 x^7+7 x^6+12 x^5+12 x^4+3 x^3+2 x^2+5 x+10$
• $y^2=2 x^8+x^6+5 x^5+9 x^4+x^3+6 x^2+6 x+8$
• $y^2=x^8+3 x^7+3 x^6+5 x^5+11 x^4+5 x^3+3 x^2+12 x+4$
• $y^2=2 x^8+x^7+10 x^6+9 x^5+12 x^3+3 x^2+9 x+6$
• $y^2=x^8+x^7+7 x^6+2 x^5+5 x^4+2 x^3+6 x^2+8 x+11$
• $y^2=x^8+x^7+3 x^6+7 x^5+3 x^4+2 x^3+2 x^2+2 x+5$
• $y^2=2 x^8+8 x^7+4 x^6+7 x^5+6 x^4+11 x^3+7 x^2+4 x$
• $y^2=x^8+12 x^7+8 x^6+6 x^5+8 x^3+6 x^2+12 x+12$
• $y^2=x^8+6 x^7+2 x^6+3 x^5+11 x^4+3 x^3+6 x^2+3 x+8$
• $y^2=x^8+4 x^7+11 x^6+4 x^5+12 x^4+7 x^2+2 x$
• $y^2=x^8+10 x^7+3 x^6+8 x^5+11 x^4+4 x^3+8 x^2+7 x+7$
• $y^2=x^7+10 x^6+11 x^5+5 x^4+11 x^3+12 x^2+3 x+10$
• $y^2=x^8+4 x^7+3 x^6+6 x^5+x^4+8 x^3+6 x^2+7 x+1$
• $y^2=2 x^8+3 x^7+x^6+2 x^5+6 x^4+3 x^3+5 x^2+10 x+4$
• $y^2=2 x^8+11 x^7+12 x^6+3 x^5+11 x^4+3 x^3+2 x^2+2 x+7$
• $y^2=x^8+9 x^7+11 x^6+11 x^5+8 x^3+5 x^2+6 x+12$
• $y^2=x^8+8 x^7+10 x^6+3 x^5+3 x^4+11 x^3+9 x^2+6 x+2$
• $y^2=x^8+9 x^7+10 x^6+5 x^5+6 x^4+8 x^3+12 x^2+12 x+11$
• $y^2=2 x^8+7 x^7+8 x^6+11 x^5+10 x^4+11 x^3+2 x^2+10 x+10$
• $y^2=x^8+2 x^7+12 x^6+7 x^5+12 x^4+5 x^3+4 x^2+2 x+1$
• $y^2=2 x^8+7 x^6+5 x^5+9 x^4+9 x^3+12 x^2+6 x+4$
• $y^2=2 x^8+7 x^7+11 x^6+9 x^5+2 x^4+2 x^3+12 x^2+8 x+1$
• $y^2=2 x^8+4 x^7+9 x^6+9 x^5+8 x^4+5 x^3+x^2+8 x+7$
• $y^2=x^8+8 x^6+7 x^5+x^4+8 x^3+11 x^2+11 x+3$
• $y^2=2 x^8+x^7+5 x^6+7 x^5+x^4+2 x^3+2 x^2+3 x+4$
• $y^2=2 x^8+4 x^7+7 x^6+12 x^5+10 x^4+4 x^3+x^2+11 x+3$
• $y^2=2 x^8+8 x^7+10 x^6+4 x^5+6 x^4+9 x^3+7 x^2+5 x+9$
• $y^2=2 x^8+4 x^7+12 x^6+8 x^5+9 x^4+9 x^3+7 x^2+3 x+1$
• $y^2=x^8+5 x^7+10 x^6+7 x^5+x^4+3 x^2+6 x+9$
• $y^2=x^8+11 x^7+12 x^6+2 x^5+3 x^4+8 x^3+3 x^2+10 x+5$
• $y^2=2 x^8+8 x^7+12 x^6+7 x^5+7 x^4+7 x^3+x^2+2 x+5$
• $y^2=x^8+5 x^7+6 x^6+11 x^5+3 x^4+9 x^3+2 x^2+10$
• $y^2=x^8+11 x^7+2 x^6+8 x^5+8 x^4+4 x^3+10 x^2+9$
• $y^2=x^8+4 x^7+2 x^6+2 x^4+8 x^3+9 x^2+4 x+1$
• $y^2=x^8+4 x^6+5 x^5+2 x^4+5 x^3+6 x^2+11 x+12$
• $y^2=2 x^8+9 x^7+8 x^6+7 x^5+3 x^4+8 x^2+4 x+4$
• $y^2=2 x^8+6 x^7+11 x^6+12 x^5+6 x^4+11 x^3+5 x^2+9 x+6$
• $y^2=x^8+7 x^7+x^6+6 x^5+10 x^4+8 x^3+3 x^2+10 x+8$
• $y^2=2 x^8+11 x^7+12 x^6+2 x^5+7 x^4+6 x^3+x^2+7 x+1$
• $y^2=2 x^8+7 x^7+9 x^4+11 x^3+7 x^2+3 x+2$
• $y^2=x^8+11 x^7+x^6+6 x^5+x^4+10 x^3+4 x^2+8 x+8$
• $y^2=x^8+9 x^7+7 x^6+8 x^5+3 x^4+9 x^3+7 x^2+10 x+2$
• $y^2=x^8+10 x^7+9 x^5+7 x^3+9 x^2+8 x+7$
• $y^2=x^8+11 x^7+4 x^6+10 x^5+6 x^4+9 x^3+3 x^2+12 x+11$
• $y^2=2 x^8+7 x^7+10 x^6+7 x^5+12 x^4+8 x^3+2 x^2+12 x+9$
• $y^2=x^8+11 x^7+5 x^6+4 x^5+x^4+7 x^3+9 x^2+10 x+7$
• $y^2=2 x^8+x^7+6 x^6+5 x^5+8 x^4+5 x^3+9 x^2+6$
• $y^2=x^8+8 x^7+12 x^5+11 x^4+6 x^3+6 x^2+8 x+5$
• $y^2=x^8+11 x^6+6 x^5+12 x^3+5 x^2+3$
• $y^2=x^8+6 x^7+8 x^6+3 x^5+11 x^4+6 x^3+6 x^2+9 x+3$
• $y^2=x^8+x^7+2 x^6+5 x^5+9 x^4+2 x^3+x^2+7 x+10$
• $y^2=2 x^8+9 x^7+2 x^6+4 x^5+7 x^4+8 x^3+2 x^2+2 x+2$
• $y^2=2 x^8+10 x^7+9 x^6+12 x^5+2 x^4+5 x^3+x^2+8 x+2$
• $y^2=x^8+2 x^7+12 x^6+4 x^5+x^4+2 x^3+8 x^2+3 x+1$
• $y^2=x^8+9 x^7+9 x^6+12 x^5+7 x^4+7 x^3+12 x^2+9 x+4$
• $y^2=2 x^8+7 x^7+4 x^6+8 x^5+5 x^4+6 x^3+10 x^2+12$
• $y^2=x^8+10 x^7+3 x^6+7 x^5+x^4+10 x^3+6 x+3$
• $y^2=2 x^8+10 x^7+4 x^6+x^5+3 x^4+7 x^3+4 x+10$
• $y^2=x^8+7 x^7+3 x^6+7 x^4+8 x^3+4 x+7$
• $y^2=x^8+8 x^7+9 x^6+12 x^5+9 x^4+7 x^3+5 x^2+12 x+6$
• $y^2=x^8+3 x^7+4 x^6+8 x^5+8 x^4+12 x^3+5 x^2+10$
• $y^2=x^8+x^7+2 x^5+6 x^4+3 x^3+4 x^2+6 x+6$
• $y^2=2 x^8+4 x^7+8 x^6+8 x^5+10 x^4+10 x^3+9 x^2+3 x+8$
• $y^2=2 x^8+8 x^7+2 x^6+11 x^5+10 x^4+9 x^3+4 x^2+12$
• $y^2=x^8+8 x^7+8 x^5+7 x^4+3 x^3+12 x+3$
• $y^2=2 x^8+12 x^7+x^6+5 x^5+4 x^4+4 x^3+x^2+8 x+5$
• $y^2=2 x^8+7 x^7+6 x^6+x^5+10 x^4+3 x^3+12 x^2+3 x+6$
• $y^2=2 x^8+9 x^7+2 x^6+4 x^4+4 x^2+5 x+1$
• $y^2=2 x^8+8 x^6+12 x^5+4 x^4+6 x^3+11 x^2+9 x+12$
• $y^2=x^8+3 x^7+2 x^6+9 x^5+11 x^4+12 x^3+9 x^2+x+8$
• $y^2=x^8+2 x^7+11 x^6+4 x^5+8 x^4+x^3+11 x^2+3 x+10$
• $y^2=x^8+5 x^7+8 x^6+9 x^5+9 x^4+8 x^3+x^2+2 x+1$
• $y^2=x^8+10 x^7+5 x^6+2 x^5+x^4+7 x^3+10 x^2+7 x+3$
• $y^2=x^8+3 x^7+6 x^6+5 x^5+5 x^4+3 x^3+2 x^2+3 x+9$
• $y^2=2 x^8+9 x^7+6 x^6+6 x^5+8 x^4+5 x^3+4 x^2+9 x+6$
• $y^2=x^8+6 x^7+12 x^6+5 x^5+x^4+10 x+9$
• $y^2=x^8+9 x^7+3 x^6+8 x^5+7 x^4+5 x^2+12 x+11$
• $y^2=x^8+6 x^7+10 x^6+x^5+5 x^4+12 x^3+3 x^2+12 x+4$
• $y^2=x^8+8 x^7+11 x^6+11 x^4+5 x^3+8 x^2+8 x+7$
• $y^2=x^8+6 x^7+11 x^6+11 x^5+4 x^4+6 x^2+11 x+4$
• $y^2=2 x^8+12 x^7+4 x^6+8 x^5+6 x^4+6 x^3+2 x+4$
• $y^2=x^8+7 x^7+4 x^6+x^4+9 x^3+5 x+6$
• $y^2=x^8+3 x^7+2 x^6+3 x^5+x^4+9 x^3+3 x^2+3 x+2$
• $y^2=x^8+x^7+6 x^6+4 x^5+5 x^4+5 x^3+9 x+11$
• $y^2=x^8+12 x^7+11 x^6+10 x^5+3 x^4+2 x^3+12 x^2+3 x+10$
• $y^2=x^8+8 x^6+x^4+4 x^3+4 x^2+5 x+7$
• $y^2=x^8+2 x^7+12 x^6+10 x^5+6 x^4+3 x^3+11 x^2+6 x+8$
• $y^2=2 x^8+3 x^7+8 x^6+12 x^5+6 x^3+7 x^2+3 x+1$
• $y^2=2 x^8+8 x^7+8 x^6+8 x^4+6 x^3+11 x^2+7 x+3$
• $y^2=x^8+4 x^7+9 x^6+3 x^5+7 x^4+6 x^3+7 x^2+10 x+1$
• $y^2=x^8+7 x^7+2 x^6+2 x^5+6 x^4+3 x^3+7 x^2+7$
• $y^2=x^8+x^7+4 x^6+7 x^5+x^4+4 x^3+3 x^2+11 x+2$
• $y^2=2 x^8+7 x^6+x^4+4 x^3+3 x^2+7 x+1$
• $y^2=x^8+5 x^7+10 x^6+12 x^5+x^4+12 x^3+5 x^2+x+1$
• $y^2=x^8+10 x^7+11 x^6+9 x^5+2 x^4+8 x^3+10 x^2+7 x+1$
• $y^2=x^8+12 x^7+12 x^6+11 x^5+12 x^4+5 x^3+12 x^2+10 x+2$
• $y^2=x^8+10 x^7+11 x^6+6 x^5+2 x^4+2 x^3+x^2+12 x+3$
• $y^2=2 x^8+6 x^7+4 x^6+11 x^5+4 x^4+7 x^3+5 x^2+2 x+8$
• $y^2=2 x^8+4 x^5+8 x^4+7 x+12$
• $y^2=2 x^8+2 x^7+8 x^6+4 x^5+8 x^4+2 x^3+5 x^2+11 x+7$
• $y^2=x^8+2 x^7+8 x^6+5 x^5+11 x^4+2 x^3+10 x^2+12 x+10$
• $y^2=x^8+4 x^7+4 x^6+4 x^5+12 x^4+5 x^3+10 x^2+4 x+7$
• $y^2=x^8+3 x^7+7 x^6+5 x^5+8 x^4+x^3+8 x^2+11 x+6$
• $y^2=2 x^8+3 x^7+8 x^6+x^5+4 x^4+9 x^3+8 x^2+9 x+4$
• $y^2=x^8+4 x^7+11 x^6+4 x^5+12 x^4+12 x^2+12 x+6$
• $y^2=x^8+8 x^7+3 x^6+7 x^5+10 x^4+4 x^3+4 x^2+7 x+3$
• $y^2=x^8+9 x^7+2 x^6+10 x^5+2 x^4+8 x^3+9 x^2+3 x+9$
• $y^2=2 x^8+11 x^7+2 x^6+12 x^5+11 x^4+7 x^3+2 x^2+5 x+3$
• $y^2=x^8+8 x^7+4 x^6+8 x^5+4 x^4+10 x^3+7 x^2+7 x+2$
• $y^2=x^8+5 x^7+12 x^6+2 x^5+x^4+x^3+10 x^2+4 x+6$
• $y^2=x^8+9 x^7+x^6+x^5+x^4+6 x^3+11 x^2+5 x+12$
• $y^2=2 x^8+2 x^7+12 x^6+3 x^5+8 x^3+9 x^2+2 x+10$
• $y^2=2 x^8+7 x^7+2 x^6+8 x^5+11 x^4+6 x^3+9 x+4$
• $y^2=2 x^8+8 x^7+9 x^6+10 x^5+3 x^4+3 x^3+4 x^2+3 x+12$
• $y^2=2 x^8+3 x^6+6 x^5+10 x^4+5 x^3+2 x^2+2 x+6$
• $y^2=2 x^8+7 x^7+10 x^6+10 x^5+12 x^4+x^3+11 x^2+2 x+6$
• $y^2=2 x^8+12 x^7+3 x^6+8 x^5+6 x^4+12 x^3+8 x^2+2 x+9$
• $y^2=x^8+5 x^7+x^6+4 x^5+12 x^4+9 x^3+7 x^2+11 x+9$
• $y^2=2 x^8+4 x^7+7 x^6+2 x^5+8 x^4+8 x^3+2 x^2+9 x+3$
• $y^2=x^8+x^7+10 x^6+5 x^5+5 x^4+7 x^3+7 x^2+12 x+10$
• $y^2=2 x^8+2 x^7+x^6+8 x^5+2 x^4+12 x^3+6 x^2+x+3$
• $y^2=x^8+11 x^7+11 x^6+3 x^5+8 x^4+10 x^3+9 x^2+2 x+1$
• $y^2=2 x^8+5 x^7+9 x^6+5 x^5+5 x^4+2 x^3+9 x^2+11 x+2$
• $y^2=2 x^8+10 x^5+x^4+11 x^3+3 x^2+5 x+11$
• $y^2=2 x^8+8 x^7+2 x^6+7 x^5+12 x^4+10 x^3+5 x^2+7 x+1$
• $y^2=2 x^8+11 x^7+7 x^6+9 x^5+4 x^4+11 x^3+2 x^2+12 x+6$
• $y^2=2 x^8+6 x^7+2 x^6+12 x^5+9 x^4+12 x^3+x^2+9 x+9$
• $y^2=x^8+5 x^7+4 x^6+4 x^5+5 x^4+11 x^3+12 x^2+10 x+12$
• $y^2=x^8+8 x^7+2 x^6+x^5+3 x^4+6 x^3+3 x^2+9 x+1$
• $y^2=x^8+11 x^7+11 x^6+8 x^5+6 x^4+11 x^3+8 x^2+12 x+8$
• $y^2=2 x^8+11 x^7+6 x^5+8 x^4+5 x^3+4 x^2+6 x+9$
• $y^2=x^8+3 x^7+8 x^6+12 x^5+x^4+8 x^3+6 x^2+11 x+12$
• $y^2=2 x^8+6 x^7+8 x^6+3 x^5+3 x^4+x^3+12 x^2+8 x+10$
• $y^2=2 x^8+10 x^7+4 x^6+3 x^5+10 x^4+4 x^3+8 x^2+x+4$
• $y^2=2 x^8+7 x^7+3 x^6+6 x^5+7 x^4+8 x^3+11 x^2+9 x+10$
• $y^2=x^8+10 x^7+5 x^5+9 x^4+10 x^3+3 x^2+5 x+1$
• $y^2=x^8+2 x^7+x^6+x^5+8 x^4+9 x^3+6 x^2+10 x+3$
• $y^2=x^8+x^7+8 x^6+11 x^5+11 x^4+12 x^3+11 x^2+9 x+6$
• $y^2=x^8+3 x^7+6 x^6+x^5+11 x^4+5 x^3+3 x^2+7 x+1$
• $y^2=x^8+11 x^6+10 x^5+12 x^4+5 x^3+4 x^2+8 x+5$
• $y^2=x^8+9 x^7+7 x^6+6 x^5+5 x^4+8 x^3+6 x^2+10 x+11$
• $y^2=2 x^8+11 x^7+9 x^6+8 x^5+8 x^4+8 x^3+9 x^2+10 x+4$
• $y^2=x^8+5 x^7+x^5+7 x^4+4 x^3+x^2+10 x+4$
• $y^2=x^8+9 x^7+x^6+5 x^4+6 x^3+10 x+2$
• $y^2=2 x^8+7 x^7+11 x^6+11 x^5+6 x^4+6 x^3+12 x^2+8 x+3$
• $y^2=2 x^8+11 x^6+7 x^5+12 x^4+4 x^3+x^2+8 x+10$
• $y^2=2 x^8+11 x^7+6 x^6+9 x^5+10 x^4+3 x^3+x^2+2 x+12$
• $y^2=x^8+x^7+9 x^6+11 x^5+9 x^4+11 x^3+x^2+2 x+6$
• $y^2=2 x^8+6 x^7+3 x^6+12 x^5+9 x^4+6 x^3+7 x^2+3 x+9$
• $y^2=x^8+11 x^7+10 x^6+3 x^5+11 x^4+8 x^3+6 x^2+4 x+5$
• $y^2=2 x^8+5 x^7+10 x^6+3 x^5+12 x^4+7 x^3+11 x^2+4 x+1$
• $y^2=x^8+10 x^7+9 x^6+3 x^5+9 x^4+4 x^2+9 x+9$
• $y^2=x^8+7 x^7+9 x^6+10 x^5+10 x^4+6 x^3+12 x^2+9 x+11$
• $y^2=2 x^8+x^6+3 x^4+6 x^3+6 x^2+12 x+5$
• $y^2=x^8+8 x^7+x^6+x^5+11 x^4+9 x^3+11 x^2+7 x+2$
• $y^2=2 x^8+6 x^7+8 x^6+3 x^5+11 x^4+10 x^3+8 x^2+11 x+5$
• $y^2=2 x^8+8 x^7+10 x^6+6 x^5+5 x^4+x^3+3 x^2+8 x+4$
• $y^2=2 x^8+x^7+12 x^6+2 x^5+6 x^4+12 x^3+5 x^2+7 x+4$
• $y^2=2 x^8+2 x^7+2 x^5+10 x^4+5 x^3+10 x^2+10 x+3$
• $y^2=2 x^8+3 x^7+7 x^6+11 x^5+4 x^4+x^3+7 x^2+x+8$
• $y^2=2 x^8+2 x^6+9 x^5+3 x^4+12 x^3+10 x^2+3 x+3$
• $y^2=x^8+x^7+7 x^6+6 x^5+3 x^4+5 x^3+x^2+7 x+11$
• $y^2=x^8+4 x^7+2 x^6+10 x^5+10 x^4+11 x^3+8 x^2+7 x+4$
• $y^2=x^8+3 x^7+x^6+6 x^5+9 x^3+9 x^2+x+12$
• $y^2=2 x^8+6 x^7+10 x^6+5 x^4+12 x^3+10 x^2+9 x+8$
• $y^2=x^8+11 x^7+4 x^6+3 x^5+6 x^4+6 x^3+5 x+8$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{13^{2}}$.

Endomorphism algebra over $\F_{13}$

The isogeny class factors as 1.13.c $\times$ 2.13.a_ac and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.13.c : \(\Q(\sqrt{-3}) \).
• 2.13.a_ac : \(\Q(\sqrt{-6}, \sqrt{7})\).

Endomorphism algebra over $\overline{\F}_{13}$

The base change of $A$ to $\F_{13^{2}}$ is 1.169.ac^2 $\times$ 1.169.w. The endomorphism algebra for each factor is:

• 1.169.ac^2 : $\mathrm{M}_{2}($\(\Q(\sqrt{-42}) \)$)$
• 1.169.w : \(\Q(\sqrt{-3}) \).

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
3.13.ac_l_e	$2$	(not in LMFDB)
3.13.ah_l_o	$3$	(not in LMFDB)
3.13.f_l_ak	$3$	(not in LMFDB)