Invariants
Base field: | $\F_{13^{2}}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 13 x )^{2}( 1 - 20 x + 169 x^{2} )$ |
$1 - 46 x + 858 x^{2} - 7774 x^{3} + 28561 x^{4}$ | |
Frobenius angles: | $0$, $0$, $\pm0.220639651288$ |
Angle rank: | $1$ (numerical) |
Jacobians: | $0$ |
This isogeny class is not simple, primitive, not ordinary, and not supersingular. It is principally polarizable.
Newton polygon
$p$-rank: | $1$ |
Slopes: | $[0, 1/2, 1/2, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $21600$ | $804384000$ | $23287205743200$ | $665413472102400000$ | $19004958441440194428000$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $124$ | $28162$ | $4824556$ | $815726878$ | $137858453164$ | $23298080542882$ | $3937376242723516$ | $665416606344634558$ | $112455406909560624604$ | $19004963774385324228802$ |
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 $\F_{13^{2}}$.
Endomorphism algebra over $\F_{13^{2}}$The isogeny class factors as 1.169.aba $\times$ 1.169.au 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 |
---|---|---|
2.169.ag_aha | $2$ | (not in LMFDB) |
2.169.g_aha | $2$ | (not in LMFDB) |
2.169.bu_bha | $2$ | (not in LMFDB) |