Invariants
| Base field: | $\F_{19}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 + 3 x + 19 x^{2} )( 1 + 4 x + 19 x^{2} )$ |
| $1 + 7 x + 50 x^{2} + 133 x^{3} + 361 x^{4}$ | |
| Frobenius angles: | $\pm0.611823923823$, $\pm0.651731832911$ |
| Angle rank: | $2$ (numerical) |
| Jacobians: | $0$ |
| Isomorphism classes: | 4 |
| Cyclic group of points: | no |
| Non-cyclic primes: | $2$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $552$ | $150144$ | $44970336$ | $16999303680$ | $6144094760952$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $27$ | $413$ | $6552$ | $130441$ | $2481357$ | $47025686$ | $893845623$ | $16984013521$ | $322686638568$ | $6131061912653$ |
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.d $\times$ 1.19.e 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.ah_by | $2$ | (not in LMFDB) |
| 2.19.ab_ba | $2$ | (not in LMFDB) |
| 2.19.b_ba | $2$ | (not in LMFDB) |