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

• Label: 2.193.abx_blt
• 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:	$1 - 49 x + 981 x^{2} - 9457 x^{3} + 37249 x^{4}$
Frobenius angles:	$\pm0.0853826055493$, $\pm0.205199049154$
Angle rank:	$2$ (numerical)
Number field:	4.0.6666597.1
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$28725$	$1371245325$	$51669514082925$	$1925161005311143125$	$71709118018795601538000$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$145$	$36811$	$7187245$	$1387515427$	$267785980150$	$51682551853939$	$9974730425992645$	$1925122953234269923$	$371548729907983826305$	$71708904873230579421886$

Jacobians and polarizations

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

• $y^2=35x^6+80x^5+192x^4+176x^3+68x^2+30x+79$
• $y^2=174x^6+91x^5+146x^4+137x^3+145x^2+173x+158$
• $y^2=57x^6+93x^5+20x^4+130x^3+88x^2+87x+52$
• $y^2=174x^6+141x^5+86x^4+119x^3+30x^2+138x+123$
• $y^2=150x^6+141x^5+97x^4+161x^3+29x^2+67x+88$
• $y^2=73x^6+181x^5+72x^4+96x^3+73x^2+141x+68$
• $y^2=111x^6+125x^5+54x^4+138x^3+9x^2+27x+99$
• $y^2=103x^6+122x^5+76x^4+184x^3+104x^2+73x+130$
• $y^2=15x^6+112x^5+12x^4+23x^3+175x^2+35x+100$
• $y^2=148x^6+171x^5+7x^4+173x^3+133x^2+183x+9$
• $y^2=167x^6+131x^5+91x^4+181x^3+120x^2+22x+163$
• $y^2=156x^6+36x^5+79x^4+47x^3+159x^2+47x+157$
• $y^2=35x^6+103x^5+131x^4+20x^3+73x^2+144x+155$
• $y^2=163x^6+9x^5+39x^4+76x^3+65x^2+78x+111$
• $y^2=125x^6+177x^5+152x^4+188x^3+43x^2+41x+132$
• $y^2=66x^6+104x^5+9x^4+118x^3+8x^2+98x$
• $y^2=14x^6+138x^5+134x^4+28x^3+169x^2+48x+62$
• $y^2=115x^6+20x^5+110x^4+127x^3+24x^2+144x+7$
• $y^2=20x^6+95x^5+69x^4+17x^3+67x^2+154x+55$
• $y^2=107x^6+186x^5+192x^4+54x^3+138x^2+128x+95$

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 4.0.6666597.1.

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.bx_blt	$2$	(not in LMFDB)