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

• Label: 2.151.abt_bfc
• 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: no

Invariants

Base field:	$\F_{151}$
Dimension:	$2$
L-polynomial:	$( 1 - 23 x + 151 x^{2} )( 1 - 22 x + 151 x^{2} )$
	$1 - 45 x + 808 x^{2} - 6795 x^{3} + 22801 x^{4}$
Frobenius angles:	$\pm0.114627783796$, $\pm0.147055957538$
Angle rank:	$2$ (numerical)
Jacobians:	$0$

This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.

Newton polygon

This isogeny class is ordinary.

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

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$16770$	$510646500$	$11845553293080$	$270284444863524000$	$6162717604231248381750$

Point counts of the (virtual) curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$107$	$22393$	$3440522$	$519892153$	$78503230877$	$11853921839578$	$1789940802930947$	$270281040015843793$	$40812436776637688582$	$6162677950491936025873$

Jacobians and polarizations

This isogeny class is principally polarizable, but does not contain a Jacobian.

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 $\times$ 1.151.aw and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.151.ax : \(\Q(\sqrt{-3}) \).
• 1.151.aw : \(\Q(\sqrt{-30}) \).

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.ab_ahw	$2$	(not in LMFDB)
2.151.b_ahw	$2$	(not in LMFDB)
2.151.bt_bfc	$2$	(not in LMFDB)
2.151.as_ig	$3$	(not in LMFDB)
2.151.ad_aem	$3$	(not in LMFDB)