Abelian variety isogeny class 2.151.abu_bfz over $\F_{151}$

• Label: 2.151.abu_bfz
• Base field: $\F_{151}$
• 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:	$\F_{151}$
Dimension:	$2$
L-polynomial:	$( 1 - 23 x + 151 x^{2} )^{2}$
	$1 - 46 x + 831 x^{2} - 6946 x^{3} + 22801 x^{4}$
Frobenius angles:	$\pm0.114627783796$, $\pm0.114627783796$
Angle rank:	$1$ (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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$16641$	$509630625$	$11841884969616$	$270274876478105625$	$6162697988644771717641$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$106$	$22348$	$3439456$	$519873748$	$78502981006$	$11853919249198$	$1789940787503506$	$270281040136414948$	$40812436782624439456$	$6162677950618152114748$

Jacobians and polarizations

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

• $y^2=121 x^6+51 x^5+35 x^4+x^3+35 x^2+51 x+121$
• $y^2=38 x^6+149 x^5+25 x^4+139 x^3+25 x^2+149 x+38$
• $y^2=94 x^6+111 x^5+51 x^4+62 x^3+51 x^2+111 x+94$
• $y^2=32 x^6+144 x^5+118 x^4+42 x^3+118 x^2+144 x+32$
• $y^2=142 x^6+99 x^5+43 x^4+80 x^3+43 x^2+99 x+142$
• $y^2=15 x^6+133 x^5+84 x^4+43 x^3+84 x^2+133 x+15$
• $y^2=32 x^6+98 x^5+149 x^4+76 x^3+74 x^2+67 x+27$
• $y^2=x^6+x^3+86$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{151}$.

Endomorphism algebra over $\F_{151}$

The isogeny class factors as 1.151.ax^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-3}) \)$)$

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
2.151.a_ait	$2$	(not in LMFDB)
2.151.bu_bfz	$2$	(not in LMFDB)
2.151.at_ic	$3$	(not in LMFDB)
2.151.ae_aff	$3$	(not in LMFDB)
2.151.i_mg	$3$	(not in LMFDB)
2.151.x_oo	$3$	(not in LMFDB)
2.151.bm_zn	$3$	(not in LMFDB)