Properties

 Label 2.193.abw_bko 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: $1 - 48 x + 950 x^{2} - 9264 x^{3} + 37249 x^{4}$ Frobenius angles: $\pm0.0484158406461$, $\pm0.235249588149$ Angle rank: $2$ (numerical) Number field: 4.0.223488.1 Galois group: $D_{4}$ Jacobians: 28

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 28 curves, and hence is principally polarizable:

• $y^2=140x^6+14x^5+108x^4+130x^3+127x^2+52x+130$
• $y^2=137x^6+133x^5+40x^4+90x^3+49x^2+111x+175$
• $y^2=192x^6+185x^5+2x^4+123x^3+14x^2+24x+192$
• $y^2=89x^6+123x^5+29x^4+155x^3+79x^2+121x+160$
• $y^2=155x^6+31x^5+69x^4+82x^3+65x^2+25x+90$
• $y^2=188x^6+57x^5+17x^4+144x^3+172x^2+124x+150$
• $y^2=45x^6+49x^5+88x^4+178x^3+167x^2+30x+81$
• $y^2=77x^6+79x^5+69x^4+135x^3+89x^2+100x+44$
• $y^2=87x^6+42x^5+111x^4+81x^3+111x^2+189x+162$
• $y^2=125x^6+110x^5+41x^4+66x^3+151x^2+11x+112$
• $y^2=159x^6+184x^5+131x^4+76x^3+132x^2+93x+83$
• $y^2=27x^6+110x^5+84x^4+182x^3+167x^2+40x+85$
• $y^2=108x^6+167x^5+87x^4+35x^3+77x^2+174x+53$
• $y^2=171x^6+74x^5+57x^4+64x^3+128x^2+93x+39$
• $y^2=61x^6+8x^5+15x^4+187x^3+x^2+108x+164$
• $y^2=95x^6+142x^5+65x^4+192x^3+157x^2+99x+93$
• $y^2=138x^6+134x^5+183x^4+31x^3+107x^2+7x+12$
• $y^2=10x^6+27x^5+67x^4+76x^3+119x^2+154x+57$
• $y^2=79x^6+65x^5+61x^4+8x^3+167x^2+141x+77$
• $y^2=94x^6+147x^5+44x^4+105x^3+152x^2+10x+51$
• $y^2=97x^6+192x^5+134x^4+176x^3+191x^2+120x+135$
• $y^2=4x^6+22x^5+105x^4+182x^3+78x^2+111x+154$
• $y^2=103x^6+149x^5+69x^4+162x^3+135x^2+46x+13$
• $y^2=149x^6+85x^5+111x^4+32x^3+53x^2+7x+171$
• $y^2=5x^6+173x^5+82x^4+107x^3+189x^2+184x+75$
• $y^2=15x^6+138x^5+120x^4+121x^3+173x^2+2x+83$
• $y^2=39x^6+57x^5+69x^4+30x^3+102x^2+4x+115$
• $y^2=66x^6+136x^5+103x^4+65x^3+26x^2+31x+182$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 28888 1372526656 51671151911704 1925139728722830336 71708939822334394340248 2671084747046999455173731392 99495243224346351430861583172184 3706098377024471399442883610134069248 138048458683997861331544807726236134956888 5142167038105890403566700086225741518220106816

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 146 36846 7187474 1387500094 267785314706 51682535700846 9974730140317970 1925122949370627838 371548729869667333778 71708904873012899182446

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
 The endomorphism algebra of this simple isogeny class is 4.0.223488.1.
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.bw_bko $2$ (not in LMFDB)