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

• Label: 2.199.abx_bma
• 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:	$1 - 49 x + 988 x^{2} - 9751 x^{3} + 39601 x^{4}$
Frobenius angles:	$\pm0.0607284856894$, $\pm0.227683861456$
Angle rank:	$2$ (numerical)
Number field:	4.0.658952.3
Galois group:	$D_{4}$
Jacobians:	$28$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$30790$	$1551508100$	$62090712867880$	$2459403784575380000$	$97393791880706733916450$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$151$	$39177$	$7878934$	$1568258073$	$312079967961$	$62103840520602$	$12358664162758519$	$2459374188757565073$	$489415464081799944346$	$97393677359498840537377$

Jacobians and polarizations

This isogeny class contains the Jacobians of 28 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=8x^6+61x^5+192x^4+113x^3+83x^2+113x+191$
• $y^2=183x^6+30x^5+60x^4+116x^3+51x^2+85x+147$
• $y^2=23x^6+62x^5+175x^4+162x^3+180x^2+171x+122$
• $y^2=44x^6+37x^5+132x^4+148x^3+147x^2+65x+127$
• $y^2=111x^6+21x^5+129x^4+198x^3+133x^2+44x+109$
• $y^2=173x^6+49x^5+60x^4+119x^3+139x^2+74x+63$
• $y^2=171x^6+121x^5+97x^4+73x^3+130x^2+165x+184$
• $y^2=21x^6+92x^5+100x^4+80x^3+132x^2+90x+78$
• $y^2=141x^6+162x^5+40x^4+126x^3+40x^2+36x+44$
• $y^2=150x^6+116x^5+126x^4+190x^3+51x^2+111x+103$
• $y^2=75x^6+118x^5+171x^4+148x^3+174x^2+25x+115$
• $y^2=176x^6+160x^5+90x^4+53x^3+180x^2+25x+77$
• $y^2=140x^6+196x^5+189x^4+94x^3+40x^2+175x+67$
• $y^2=189x^6+195x^5+33x^4+27x^3+41x^2+111x+76$
• $y^2=143x^6+150x^5+196x^4+129x^3+60x^2+73x+171$
• $y^2=85x^6+69x^5+136x^4+110x^3+38x^2+122x+67$
• $y^2=87x^6+32x^5+169x^4+159x^3+137x^2+74x+146$
• $y^2=22x^6+186x^5+181x^4+127x^3+174x^2+106x+118$
• $y^2=192x^6+98x^5+108x^4+170x^3+9x^2+119x+119$
• $y^2=174x^6+54x^5+31x^4+109x^3+66x^2+129x+136$
• $y^2=168x^6+127x^5+166x^4+178x^3+72x^2+163x+128$
• $y^2=56x^6+96x^5+133x^4+132x^3+6x^2+86x+136$
• $y^2=138x^6+92x^5+70x^4+31x^3+31x^2+53x+60$
• $y^2=182x^6+186x^5+155x^4+8x^3+14x^2+154x+73$
• $y^2=78x^6+120x^5+109x^4+70x^3+145x^2+48x+70$
• $y^2=191x^6+82x^5+32x^4+55x^3+89x^2+87x+157$
• $y^2=14x^6+166x^5+113x^4+140x^3+152x^2+27x+67$
• $y^2=26x^6+63x^5+60x^4+146x^3+60x^2+97x+116$

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 4.0.658952.3.

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_bma	$2$	(not in LMFDB)