Invariants
| Base field: | $\F_{157}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 42 x + 740 x^{2} - 6594 x^{3} + 24649 x^{4}$ |
| Frobenius angles: | $\pm0.0389047198548$, $\pm0.260482049894$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.11246400.2 |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $18754$ | $600615604$ | $14973630361906$ | $369148442963009616$ | $9099045914923550451634$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $116$ | $24366$ | $3869264$ | $607578550$ | $95388845936$ | $14976064561902$ | $2351243131510340$ | $369145192721063134$ | $57955795533962867828$ | $9099059901035935172286$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=57x^6+34x^5+92x^4+107x^3+87x^2+24x+28$
- $y^2=77x^6+132x^5+81x^4+96x^3+142x^2+131x$
- $y^2=23x^6+114x^5+5x^4+79x^3+20x^2+107x+118$
- $y^2=74x^6+93x^5+90x^4+95x^3+39x^2+119x+95$
- $y^2=144x^6+12x^5+117x^4+144x^3+124x^2+125x+91$
- $y^2=141x^6+38x^5+17x^4+119x^3+10x^2+24x+11$
- $y^2=19x^6+13x^5+78x^4+84x^3+19x^2+29x+128$
- $y^2=10x^6+146x^5+61x^4+134x^3+13x^2+40x+51$
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 4.0.11246400.2. |
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 |
|---|---|---|
| 2.157.bq_bcm | $2$ | (not in LMFDB) |