Invariants
| Base field: | $\F_{19}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 6 x + 19 x^{2} )( 1 - 5 x + 19 x^{2} )$ |
| $1 - 11 x + 68 x^{2} - 209 x^{3} + 361 x^{4}$ | |
| Frobenius angles: | $\pm0.258380448083$, $\pm0.305569972467$ |
| Angle rank: | $2$ (numerical) |
| Jacobians: | $0$ |
| Isomorphism classes: | 4 |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.
Newton polygon
This isogeny class is ordinary.
| $p$-rank: | $2$ |
| Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $210$ | $136500$ | $49041720$ | $17149860000$ | $6135129011550$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $9$ | $377$ | $7146$ | $131593$ | $2477739$ | $47031842$ | $893768241$ | $16983262993$ | $322687909134$ | $6131072423177$ |
Jacobians and polarizations
This isogeny class is principally polarizable, but does not contain a Jacobian.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{19}$.
Endomorphism algebra over $\F_{19}$| The isogeny class factors as 1.19.ag $\times$ 1.19.af and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
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 |
|---|---|---|
| 2.19.ab_i | $2$ | (not in LMFDB) |
| 2.19.b_i | $2$ | (not in LMFDB) |
| 2.19.l_cq | $2$ | (not in LMFDB) |