Abelian variety isogeny class 2.211.abz_bpb over $\F_{211}$

• Label: 2.211.abz_bpb
• Base field: $\F_{211}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: yes
• Geometrically simple: yes
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{211}$
Dimension:	$2$
L-polynomial:	$1 - 51 x + 1067 x^{2} - 10761 x^{3} + 44521 x^{4}$
Frobenius angles:	$\pm0.0941054562723$, $\pm0.205427889818$
Angle rank:	$2$ (numerical)
Number field:	4.0.9647757.1
Galois group:	$D_{4}$
Jacobians:	$20$

This isogeny class is simple and geometrically 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$34777$	$1961457577$	$88230139951963$	$3928880191673854125$	$174914481495549691184752$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$161$	$44055$	$9392249$	$1982161171$	$418228371176$	$88245957413787$	$18619893445864151$	$3928797479491855891$	$828976267940163952979$	$174913992535405809150630$

Jacobians and polarizations

This isogeny class contains the Jacobians of 20 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=102x^6+18x^5+46x^4+69x^3+18x^2+189x+74$
• $y^2=4x^6+204x^5+156x^4+56x^3+37x^2+177x+6$
• $y^2=202x^6+46x^5+22x^4+139x^3+16x^2+145x+61$
• $y^2=68x^6+86x^5+106x^4+88x^3+79x^2+185x+146$
• $y^2=10x^6+137x^5+29x^4+152x^3+27x^2+59x+66$
• $y^2=68x^6+187x^5+208x^4+75x^3+186x^2+102x+132$
• $y^2=118x^6+13x^5+4x^4+103x^3+58x^2+36x+150$
• $y^2=40x^6+18x^5+124x^4+198x^3+204x^2+64x+198$
• $y^2=110x^6+111x^5+196x^4+101x^3+156x^2+86x+175$
• $y^2=45x^6+87x^5+133x^4+101x^3+120x^2+20x+139$
• $y^2=150x^6+14x^5+107x^4+159x^3+112x^2+33x+125$
• $y^2=77x^6+173x^5+146x^4+93x^3+3x^2+25x+198$
• $y^2=25x^6+101x^5+66x^4+110x^3+152x^2+156x+22$
• $y^2=72x^6+58x^5+88x^4+185x^3+191x^2+142x+160$
• $y^2=197x^6+8x^5+18x^4+170x^3+84x^2+107x+71$
• $y^2=204x^6+64x^5+107x^4+203x^3+115x^2+37x+163$
• $y^2=72x^6+68x^5+82x^4+189x^3+124x^2+205x+4$
• $y^2=96x^6+166x^5+155x^4+66x^3+162x^2+191x+20$
• $y^2=86x^6+76x^5+110x^4+29x^3+78x^2+209x+135$
• $y^2=203x^6+145x^5+166x^4+179x^3+37x^2+54x+11$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{211}$.

Endomorphism algebra over $\F_{211}$

The endomorphism algebra of this simple isogeny class is 4.0.9647757.1.

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
2.211.bz_bpb	$2$	(not in LMFDB)