Invariants
| Base field: | $\F_{113}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 38 x + 584 x^{2} - 4294 x^{3} + 12769 x^{4}$ |
| Frobenius angles: | $\pm0.0711049505690$, $\pm0.198261056171$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.491328.3 |
| Galois group: | $D_{4}$ |
| Jacobians: | $6$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $9022$ | $159563092$ | $2080253577454$ | $26585146946632144$ | $339459545799370847422$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $76$ | $12494$ | $1441720$ | $163051686$ | $18424504136$ | $2081953482302$ | $235260558414524$ | $26584441911916414$ | $3004041936758781916$ | $339456738978109291934$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 6 curves (of which all are hyperelliptic):
- $y^2=44 x^6+85 x^5+94 x^4+25 x^3+53 x^2+99 x+72$
- $y^2=94 x^6+28 x^5+93 x^4+23 x^3+66 x^2+22 x+107$
- $y^2=38 x^6+65 x^5+90 x^4+56 x^3+64 x^2+67 x+17$
- $y^2=5 x^6+15 x^5+108 x^4+109 x^3+88 x^2+54 x+107$
- $y^2=68 x^6+65 x^5+31 x^4+86 x^3+35 x^2+77 x+102$
- $y^2=3 x^6+57 x^5+91 x^4+111 x^3+75 x^2+49 x+63$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{113}$.
Endomorphism algebra over $\F_{113}$| The endomorphism algebra of this simple isogeny class is 4.0.491328.3. |
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 |
|---|---|---|
| 2.113.bm_wm | $2$ | (not in LMFDB) |