Invariants
Base field: | $\F_{23}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 7 x + 23 x^{2} )( 1 - 5 x + 23 x^{2} )$ |
$1 - 12 x + 81 x^{2} - 276 x^{3} + 529 x^{4}$ | |
Frobenius angles: | $\pm0.239612957690$, $\pm0.325452467839$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $3$ |
Isomorphism classes: | 4 |
This isogeny class is not 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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $323$ | $290377$ | $152471504$ | $78778408969$ | $41440341210323$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $12$ | $548$ | $12528$ | $281508$ | $6438492$ | $148016558$ | $3404688852$ | $78310623556$ | $1801152913104$ | $41426516059268$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 3 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=10x^6+19x^5+21x^4+22x^3+19x^2+7x+11$
- $y^2=21x^6+11x^5+x^4+13x^3+13x^2+19x+22$
- $y^2=11x^6+21x^5+5x^4+3x^3+22x^2+22x+15$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{23}$.
Endomorphism algebra over $\F_{23}$The isogeny class factors as 1.23.ah $\times$ 1.23.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 |
---|---|---|
2.23.ac_l | $2$ | (not in LMFDB) |
2.23.c_l | $2$ | (not in LMFDB) |
2.23.m_dd | $2$ | (not in LMFDB) |