Abelian variety isogeny class 2.149.abu_bfu over $\F_{149}$

• Label: 2.149.abu_bfu
• Base field: $\F_{149}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{149}$
Dimension:	$2$
L-polynomial:	$( 1 - 24 x + 149 x^{2} )( 1 - 22 x + 149 x^{2} )$
	$1 - 46 x + 826 x^{2} - 6854 x^{3} + 22201 x^{4}$
Frobenius angles:	$\pm0.0586410025892$, $\pm0.142720447332$
Angle rank:	$2$ (numerical)
Jacobians:	$8$

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:	$2$
Slopes:	$[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$16128$	$482678784$	$10929601638144$	$242923659611996160$	$5393401334367499208448$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$104$	$21738$	$3304040$	$492861326$	$73439784904$	$10942529570586$	$1630436519748616$	$242935033543282846$	$36197319888207251240$	$5393400662136091679178$

Jacobians and polarizations

This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=27x^6+12x^5+127x^4+84x^3+127x^2+12x+27$
• $y^2=45x^6+102x^5+47x^4+85x^3+47x^2+102x+45$
• $y^2=77x^6+10x^5+90x^4+44x^3+137x^2+126x+115$
• $y^2=71x^6+101x^5+54x^4+48x^3+69x^2+32x+83$
• $y^2=43x^6+6x^5+40x^4+130x^3+40x^2+6x+43$
• $y^2=60x^6+27x^5+86x^4+81x^3+88x^2+2x+70$
• $y^2=55x^6+138x^5+34x^4+27x^3+34x^2+138x+55$
• $y^2=27x^6+25x^5+66x^4+58x^3+146x^2+49x+32$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{149}$.

Endomorphism algebra over $\F_{149}$

The isogeny class factors as 1.149.ay $\times$ 1.149.aw and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.149.ay : \(\Q(\sqrt{-5}) \).
• 1.149.aw : \(\Q(\sqrt{-7}) \).

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
2.149.ac_aiw	$2$	(not in LMFDB)
2.149.c_aiw	$2$	(not in LMFDB)
2.149.bu_bfu	$2$	(not in LMFDB)