Invariants
Base field: | $\F_{157}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 44 x + 790 x^{2} - 6908 x^{3} + 24649 x^{4}$ |
Frobenius angles: | $\pm0.0432998700335$, $\pm0.222724578300$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.48128.1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $18488$ | $598863296$ | $14969772221432$ | $369147777231420416$ | $9099069298294218900408$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $114$ | $24294$ | $3868266$ | $607577454$ | $95389091074$ | $14976070335894$ | $2351243203406778$ | $369145193068865118$ | $57955795527626372370$ | $9099059900855349312454$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 28 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=79x^6+51x^5+42x^4+116x^3+13x^2+15x+109$
- $y^2=75x^6+52x^5+10x^4+156x^3+85x^2+52x+99$
- $y^2=138x^6+60x^5+49x^4+91x^3+60x^2+49x+55$
- $y^2=72x^6+13x^5+73x^4+7x^3+107x^2+28x+104$
- $y^2=92x^6+59x^5+51x^4+120x^3+103x^2+109x+68$
- $y^2=107x^6+17x^5+89x^4+x^3+143x^2+88x+3$
- $y^2=24x^6+51x^5+87x^4+26x^3+11x^2+54x+83$
- $y^2=27x^6+89x^5+31x^4+40x^3+65x^2+34x+82$
- $y^2=39x^6+50x^5+54x^4+74x^3+27x^2+47x+53$
- $y^2=144x^6+88x^5+100x^4+59x^3+79x^2+53x+41$
- $y^2=76x^6+34x^5+45x^4+64x^3+109x^2+132x+63$
- $y^2=15x^6+42x^5+148x^4+153x^3+18x^2+52x+146$
- $y^2=87x^6+151x^5+15x^4+124x^3+26x^2+25x+58$
- $y^2=119x^6+22x^5+149x^4+102x^3+32x^2+40x$
- $y^2=8x^6+99x^5+155x^4+79x^3+9x^2+86x+18$
- $y^2=57x^6+115x^5+20x^4+49x^3+110x^2+64x+88$
- $y^2=24x^6+86x^5+59x^4+30x^3+35x^2+101x+137$
- $y^2=153x^6+121x^5+76x^4+23x^3+20x^2+79x+149$
- $y^2=73x^6+51x^5+141x^3+108x^2+19x+62$
- $y^2=150x^6+3x^5+12x^4+28x^3+94x^2+133x+84$
- $y^2=79x^6+131x^5+140x^4+26x^3+80x^2+55x+88$
- $y^2=88x^6+52x^5+78x^4+148x^3+138x^2+22x+48$
- $y^2=91x^6+105x^5+68x^4+35x^3+7x^2+140x+92$
- $y^2=19x^6+20x^5+126x^4+127x^3+13x^2+103x+5$
- $y^2=129x^6+131x^5+31x^4+59x^3+102x^2+35x+149$
- $y^2=29x^6+99x^5+108x^4+61x^3+36x^2+4x+32$
- $y^2=50x^6+76x^5+92x^4+116x^3+76x^2+86x+90$
- $y^2=143x^6+12x^5+29x^4+46x^3+64x^2+100x+52$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{157}$.
Endomorphism algebra over $\F_{157}$The endomorphism algebra of this simple isogeny class is 4.0.48128.1. |
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 |
---|---|---|
2.157.bs_bek | $2$ | (not in LMFDB) |