Properties

 Label 2.193.abx_blq Base Field $\F_{193}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

Invariants

 Base field: $\F_{193}$ Dimension: $2$ L-polynomial: $1 - 49 x + 978 x^{2} - 9457 x^{3} + 37249 x^{4}$ Frobenius angles: $\pm0.0549247165904$, $\pm0.216032287700$ Angle rank: $2$ (numerical) Number field: 4.0.7540236.1 Galois group: $D_{4}$ Jacobians: 16

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

 $p$-rank: $2$ Slopes: $[0, 0, 1, 1]$

Point counts

This isogeny class contains the Jacobians of 16 curves, and hence is principally polarizable:

• $y^2=8x^6+58x^5+191x^4+29x^3+156x^2+104x+88$
• $y^2=42x^6+86x^5+131x^4+72x^3+36x^2+61x+78$
• $y^2=34x^6+185x^5+185x^4+101x^3+145x^2+7x+39$
• $y^2=172x^6+107x^5+97x^4+156x^3+150x^2+168x+53$
• $y^2=151x^6+31x^5+91x^4+180x^3+136x^2+191x+2$
• $y^2=164x^6+6x^5+73x^4+128x^3+57x^2+133x+62$
• $y^2=163x^6+172x^5+147x^4+121x^3+112x^2+18x+26$
• $y^2=141x^6+69x^5+100x^4+118x^3+159x^2+97x+141$
• $y^2=44x^6+137x^5+124x^4+118x^3+190x^2+69x+86$
• $y^2=176x^6+x^5+60x^4+161x^3+28x^2+21x+164$
• $y^2=52x^6+169x^5+139x^4+93x^3+35x^2+182x+141$
• $y^2=174x^6+16x^5+91x^4+30x^3+118x^2+70x+136$
• $y^2=128x^6+111x^5+135x^4+76x^3+60x^2+124x+45$
• $y^2=7x^6+13x^5+23x^4+39x^3+60x^2+7x+52$
• $y^2=99x^6+120x^5+157x^4+55x^3+188x^2+2x+190$
• $y^2=121x^6+116x^5+143x^4+113x^3+166x^2+172x+71$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 28722 1371015948 51666339579336 1925137335886408704 71708993036323845168882 2671085062389232685249740800 99495244292660060367489895051698 3706098379333666796779308738555654144 138048458685872388295481042495765884394184 5142167038097249931799228255258737997414454028

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 145 36805 7186804 1387498369 267785513425 51682541802370 9974730247419985 1925122950570133249 371548729874712505012 71708904872892405475525

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
 The endomorphism algebra of this simple isogeny class is 4.0.7540236.1.
All geometric endomorphisms are defined over $\F_{193}$.

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_blq $2$ (not in LMFDB)