Abelian variety isogeny class 2.199.abx_bmf over $\F_{199}$

• Label: 2.199.abx_bmf
• Base field: $\F_{199}$
• 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:	$\F_{199}$
Dimension:	$2$
L-polynomial:	$1 - 49 x + 993 x^{2} - 9751 x^{3} + 39601 x^{4}$
Frobenius angles:	$\pm0.101497698060$, $\pm0.211547002897$
Angle rank:	$2$ (numerical)
Number field:	4.0.10445085.2
Galois group:	$D_{4}$
Jacobians:	$32$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$30795$	$1551914025$	$62096512064265$	$2459448027342682125$	$97394028523549995087600$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$151$	$39187$	$7879669$	$1568286283$	$312080726236$	$62103856340167$	$12358664429084299$	$2459374192375886563$	$489415464119446342261$	$97393677359734970649502$

Jacobians and polarizations

This isogeny class contains the Jacobians of 32 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=171x^6+95x^5+46x^4+183x^3+123x^2+13x+146$
• $y^2=24x^6+31x^5+178x^4+16x^3+13x^2+141x+91$
• $y^2=135x^6+28x^5+50x^4+17x^3+175x^2+195x+10$
• $y^2=117x^6+65x^5+66x^4+54x^3+145x^2+196x+26$
• $y^2=87x^6+119x^5+114x^4+192x^3+46x^2+113x+135$
• $y^2=63x^6+133x^5+53x^4+25x^3+79x^2+102x+139$
• $y^2=126x^6+90x^5+35x^4+106x^3+20x^2+152x+54$
• $y^2=152x^6+105x^5+178x^4+106x^3+72x^2+155x+171$
• $y^2=104x^6+169x^5+4x^4+146x^3+97x^2+18x+48$
• $y^2=27x^6+52x^5+171x^4+96x^3+45x^2+189x+85$
• $y^2=18x^6+70x^5+102x^4+159x^3+164x^2+144x+108$
• $y^2=84x^6+101x^5+158x^4+146x^3+189x^2+103x+186$
• $y^2=135x^6+50x^5+43x^4+177x^3+145x^2+130x+76$
• $y^2=109x^6+13x^5+152x^4+151x^3+84x^2+198x+158$
• $y^2=12x^6+56x^5+10x^4+176x^3+147x^2+10x+48$
• $y^2=117x^6+57x^5+23x^4+7x^3+166x^2+93x+17$
• $y^2=109x^6+75x^5+7x^4+182x^3+57x^2+71x+92$
• $y^2=20x^6+195x^5+69x^4+19x^3+124x^2+99x+25$
• $y^2=55x^6+173x^5+50x^4+133x^3+148x^2+194x+97$
• $y^2=187x^6+103x^5+39x^4+134x^3+168x^2+198x+50$
• and

• $y^2=63x^6+56x^5+135x^4+7x^3+106x^2+41x+99$
• $y^2=94x^6+178x^5+189x^4+106x^3+55x^2+6x+119$
• $y^2=17x^6+189x^5+67x^4+40x^3+185x^2+128x+87$
• $y^2=127x^6+187x^5+143x^4+61x^3+106x^2+102x+18$
• $y^2=154x^6+146x^5+108x^4+127x^3+103x^2+112x+187$
• $y^2=43x^6+135x^5+18x^4+158x^3+153x^2+131x+49$
• $y^2=104x^6+141x^5+117x^4+30x^3+26x^2+113x+85$
• $y^2=59x^6+127x^5+62x^4+86x^3+53x^2+150x+97$
• $y^2=138x^6+156x^5+114x^4+131x^3+181x^2+158x+94$
• $y^2=70x^6+48x^5+17x^4+121x^3+143x+169$
• $y^2=20x^6+127x^5+22x^4+143x^3+122x^2+167x+45$
• $y^2=80x^6+125x^5+194x^4+8x^3+159x^2+180x+39$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{199}$.

Endomorphism algebra over $\F_{199}$

The endomorphism algebra of this simple isogeny class is 4.0.10445085.2.

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
2.199.bx_bmf	$2$	(not in LMFDB)