Abelian variety isogeny class 2.193.abv_bjm over $\F_{193}$

• Label: 2.193.abv_bjm
• Base field: $\F_{193}$
• 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:	$\F_{193}$
Dimension:	$2$
L-polynomial:	$1 - 47 x + 922 x^{2} - 9071 x^{3} + 37249 x^{4}$
Frobenius angles:	$\pm0.0430529292584$, $\pm0.252871153020$
Angle rank:	$2$ (numerical)
Number field:	4.0.23305100.1
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$29054$	$1373963660$	$51675102260096$	$1925137645825145600$	$71708875661368639450494$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$147$	$36885$	$7188024$	$1387498593$	$267785075107$	$51682529873730$	$9974730059420259$	$1925122948848287553$	$371548729875056935512$	$71708904873211218207925$

Jacobians and polarizations

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

• $y^2=12x^6+158x^5+90x^4+57x^3+99x^2+26x+136$
• $y^2=115x^6+139x^5+69x^4+164x^3+51x^2+171x+73$
• $y^2=77x^6+94x^5+60x^4+139x^3+52x^2+113x+188$
• $y^2=58x^6+24x^5+97x^4+38x^3+120x^2+163x+17$
• $y^2=74x^6+91x^5+160x^4+24x^3+27x^2+127x+101$
• $y^2=35x^6+171x^5+104x^4+19x^3+82x^2+114x+164$
• $y^2=117x^6+119x^5+158x^4+31x^3+116x^2+123x+93$
• $y^2=44x^6+158x^5+39x^4+133x^3+121x^2+99x+61$
• $y^2=77x^6+135x^5+60x^4+65x^3+105x^2+61x+106$
• $y^2=169x^6+183x^5+8x^4+36x^3+49x^2+98x+24$
• $y^2=136x^6+7x^5+160x^4+37x^3+65x^2+105x+169$
• $y^2=34x^6+153x^5+54x^4+148x^3+157x^2+13x+29$
• $y^2=102x^6+4x^5+191x^4+15x^3+62x^2+87x+40$
• $y^2=185x^6+183x^5+25x^4+71x^3+10x^2+142x+85$
• $y^2=142x^6+148x^5+6x^4+115x^3+32x^2+57x+45$
• $y^2=57x^6+20x^5+35x^4+11x^3+81x^2+98x+45$
• $y^2=151x^6+37x^5+133x^4+55x^3+132x^2+174x+192$
• $y^2=76x^6+55x^5+36x^4+140x^3+10x^2+95x+114$
• $y^2=85x^6+138x^5+27x^4+105x^3+89x^2+34x+50$
• $y^2=76x^6+106x^5+25x^4+104x^3+166x^2+167x+112$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{193}$.

Endomorphism algebra over $\F_{193}$

The endomorphism algebra of this simple isogeny class is 4.0.23305100.1.

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
2.193.bv_bjm	$2$	(not in LMFDB)