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

• Label: 2.199.aby_bng
• 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:	$1 - 50 x + 1020 x^{2} - 9950 x^{3} + 39601 x^{4}$
Frobenius angles:	$\pm0.103608408825$, $\pm0.191337995159$
Angle rank:	$2$ (numerical)
Number field:	4.0.2984256.4
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$30622$	$1550146884$	$62089273182742$	$2459433165523064016$	$97394042571542335408102$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$150$	$39142$	$7878750$	$1568276806$	$312080771250$	$62103860564182$	$12358664531197050$	$2459374193945044798$	$489415464133902979350$	$97393677359714003455702$

Jacobians and polarizations

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

• $y^2=55x^6+95x^5+22x^4+6x^3+99x^2+156x+81$
• $y^2=142x^6+103x^5+44x^4+117x^3+159x^2+187x+42$
• $y^2=116x^6+88x^5+163x^4+104x^3+26x^2+95x+154$
• $y^2=109x^6+158x^5+95x^4+31x^3+191x^2+168x+192$
• $y^2=78x^6+41x^5+31x^4+172x^3+68x^2+116x+73$
• $y^2=173x^6+125x^5+9x^4+96x^3+156x^2+98x+36$
• $y^2=41x^6+165x^5+148x^4+34x^3+111x^2+141x+95$
• $y^2=54x^6+36x^5+37x^4+82x^3+142x^2+140x+156$
• $y^2=121x^6+34x^5+81x^4+160x^3+126x^2+165x+46$
• $y^2=49x^6+187x^5+89x^4+3x^3+65x^2+193x+132$
• $y^2=88x^6+70x^5+74x^4+64x^3+47x^2+196x+101$
• $y^2=82x^6+186x^5+50x^4+188x^3+63x^2+41x+6$
• $y^2=96x^6+132x^5+67x^4+139x^3+85x^2+119x+157$
• $y^2=96x^6+128x^5+180x^4+172x^3+23x^2+103x+41$
• $y^2=198x^6+70x^5+89x^4+14x^3+63x^2+152x+146$
• $y^2=117x^6+15x^5+25x^4+96x^3+188x^2+77x+54$
• $y^2=6x^6+152x^5+14x^4+130x^3+13x^2+71x+12$
• $y^2=158x^6+97x^5+82x^4+84x^3+83x^2+68x+93$
• $y^2=27x^6+78x^5+179x^4+101x^3+141x^2+181x+52$
• $y^2=100x^6+3x^5+156x^4+39x^3+84x^2+51x+14$
• and

• $y^2=150x^6+146x^5+115x^4+188x^3+135x^2+64x+80$
• $y^2=194x^6+109x^5+10x^4+116x^3+34x^2+102x+91$
• $y^2=125x^6+184x^5+191x^4+114x^3+196x^2+34x+81$
• $y^2=177x^6+120x^5+13x^4+156x^3+188x^2+198x+135$
• $y^2=62x^6+104x^5+72x^4+25x^3+96x^2+27x+68$
• $y^2=129x^6+68x^5+6x^4+131x^3+186x^2+36x+64$
• $y^2=30x^6+145x^5+55x^4+84x^3+26x^2+99x+71$
• $y^2=167x^6+46x^5+145x^4+4x^3+93x^2+28x+174$
• $y^2=98x^6+156x^5+124x^4+197x^3+67x^2+50x$
• $y^2=18x^6+27x^5+121x^4+14x^3+185x^2+164x+16$
• $y^2=11x^6+119x^5+104x^4+47x^3+136x^2+100x+27$
• $y^2=171x^6+134x^5+70x^4+16x^3+127x^2+27x+44$

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 4.0.2984256.4.

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.by_bng	$2$	(not in LMFDB)