Invariants
Base field: | $\F_{151}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 43 x + 763 x^{2} - 6493 x^{3} + 22801 x^{4}$ |
Frobenius angles: | $\pm0.127932556465$, $\pm0.188722117555$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.435725.2 |
Galois group: | $D_{4}$ |
Jacobians: | $8$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $17029$ | $512589929$ | $11851992849475$ | $270298932124668509$ | $6162739940459429993584$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $109$ | $22479$ | $3442393$ | $519920019$ | $78503515404$ | $11853923018403$ | $1789940775049459$ | $270281039132147859$ | $40812436761094376803$ | $6162677950289800155454$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=121x^6+18x^5+135x^4+91x^3+12x^2+134x+15$
- $y^2=64x^6+78x^5+122x^4+43x^3+8x^2+25x+95$
- $y^2=11x^6+71x^5+58x^4+107x^3+23x^2+17x+139$
- $y^2=122x^6+25x^5+111x^4+53x^3+146x^2+140x+51$
- $y^2=66x^6+66x^5+15x^4+66x^3+116x^2+4x+54$
- $y^2=134x^6+138x^5+40x^4+62x^3+53x^2+137x+27$
- $y^2=129x^6+85x^5+146x^4+26x^3+93x^2+40x+84$
- $y^2=135x^6+65x^5+33x^4+11x^3+11x^2+80x+79$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{151}$.
Endomorphism algebra over $\F_{151}$The endomorphism algebra of this simple isogeny class is 4.0.435725.2. |
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 |
---|---|---|
2.151.br_bdj | $2$ | (not in LMFDB) |