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, 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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $28888$ | $1372526656$ | $51671151911704$ | $1925139728722830336$ | $71708939822334394340248$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $146$ | $36846$ | $7187474$ | $1387500094$ | $267785314706$ | $51682535700846$ | $9974730140317970$ | $1925122949370627838$ | $371548729869667333778$ | $71708904873012899182446$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 28 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=140x^6+14x^5+108x^4+130x^3+127x^2+52x+130$
- $y^2=137x^6+133x^5+40x^4+90x^3+49x^2+111x+175$
- $y^2=192x^6+185x^5+2x^4+123x^3+14x^2+24x+192$
- $y^2=89x^6+123x^5+29x^4+155x^3+79x^2+121x+160$
- $y^2=155x^6+31x^5+69x^4+82x^3+65x^2+25x+90$
- $y^2=188x^6+57x^5+17x^4+144x^3+172x^2+124x+150$
- $y^2=45x^6+49x^5+88x^4+178x^3+167x^2+30x+81$
- $y^2=77x^6+79x^5+69x^4+135x^3+89x^2+100x+44$
- $y^2=87x^6+42x^5+111x^4+81x^3+111x^2+189x+162$
- $y^2=125x^6+110x^5+41x^4+66x^3+151x^2+11x+112$
- $y^2=159x^6+184x^5+131x^4+76x^3+132x^2+93x+83$
- $y^2=27x^6+110x^5+84x^4+182x^3+167x^2+40x+85$
- $y^2=108x^6+167x^5+87x^4+35x^3+77x^2+174x+53$
- $y^2=171x^6+74x^5+57x^4+64x^3+128x^2+93x+39$
- $y^2=61x^6+8x^5+15x^4+187x^3+x^2+108x+164$
- $y^2=95x^6+142x^5+65x^4+192x^3+157x^2+99x+93$
- $y^2=138x^6+134x^5+183x^4+31x^3+107x^2+7x+12$
- $y^2=10x^6+27x^5+67x^4+76x^3+119x^2+154x+57$
- $y^2=79x^6+65x^5+61x^4+8x^3+167x^2+141x+77$
- $y^2=94x^6+147x^5+44x^4+105x^3+152x^2+10x+51$
- $y^2=97x^6+192x^5+134x^4+176x^3+191x^2+120x+135$
- $y^2=4x^6+22x^5+105x^4+182x^3+78x^2+111x+154$
- $y^2=103x^6+149x^5+69x^4+162x^3+135x^2+46x+13$
- $y^2=149x^6+85x^5+111x^4+32x^3+53x^2+7x+171$
- $y^2=5x^6+173x^5+82x^4+107x^3+189x^2+184x+75$
- $y^2=15x^6+138x^5+120x^4+121x^3+173x^2+2x+83$
- $y^2=39x^6+57x^5+69x^4+30x^3+102x^2+4x+115$
- $y^2=66x^6+136x^5+103x^4+65x^3+26x^2+31x+182$
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 4.0.223488.1. |
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.bw_bko | $2$ | (not in LMFDB) |