Invariants
Base field: | $\F_{173}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 45 x + 841 x^{2} - 7785 x^{3} + 29929 x^{4}$ |
Frobenius angles: | $\pm0.0590786929552$, $\pm0.240534632429$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.191725.1 |
Galois group: | $D_{4}$ |
Jacobians: | $35$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $22941$ | $885545541$ | $26803859468409$ | $802372908521883861$ | $24013832817305137718736$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $129$ | $29587$ | $5176773$ | $895760371$ | $154964053194$ | $26808750598723$ | $4637914215583953$ | $802359176581200163$ | $138808137858232439709$ | $24013807852607341620022$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 35 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=4x^6+51x^5+66x^4+108x^3+81x^2+111x+75$
- $y^2=160x^6+48x^5+13x^4+161x^3+109x^2+89x+82$
- $y^2=166x^6+68x^5+170x^4+130x^3+51x^2+73x+128$
- $y^2=138x^6+134x^5+51x^4+58x^3+8x^2+33x+106$
- $y^2=143x^6+41x^5+156x^4+154x^3+25x^2+35x+51$
- $y^2=128x^6+143x^5+4x^4+145x^3+96x^2+10x+54$
- $y^2=21x^6+118x^5+72x^4+83x^3+76x^2+75x+21$
- $y^2=51x^6+148x^5+165x^4+164x^3+121x^2+18x+90$
- $y^2=93x^6+49x^5+75x^4+118x^3+25x^2+54x+8$
- $y^2=8x^6+x^5+154x^4+54x^3+48x^2+30x+39$
- $y^2=104x^6+34x^5+141x^4+8x^3+163x^2+168x+65$
- $y^2=95x^6+172x^5+17x^4+19x^3+88x^2+172x+91$
- $y^2=48x^6+14x^5+40x^4+31x^3+122x^2+154x+91$
- $y^2=32x^6+150x^5+112x^4+112x^3+33x^2+155x+97$
- $y^2=59x^6+48x^5+144x^4+117x^3+116x^2+161x+141$
- $y^2=71x^6+44x^5+93x^4+68x^3+129x^2+136x+123$
- $y^2=20x^6+109x^5+112x^4+138x^3+16x^2+162x+137$
- $y^2=11x^6+28x^5+85x^4+105x^3+123x^2+4x+89$
- $y^2=163x^6+162x^5+64x^4+161x^3+88x^2+112x+75$
- $y^2=145x^6+81x^5+133x^4+126x^3+10x^2+137x+124$
- and 15 more
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{173}$.
Endomorphism algebra over $\F_{173}$The endomorphism algebra of this simple isogeny class is 4.0.191725.1. |
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 |
---|---|---|
2.173.bt_bgj | $2$ | (not in LMFDB) |