Invariants
Base field: | $\F_{23}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 12 x + 77 x^{2} - 276 x^{3} + 529 x^{4}$ |
Frobenius angles: | $\pm0.171291584331$, $\pm0.371639008133$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.47025.1 |
Galois group: | $D_{4}$ |
Jacobians: | $16$ |
Isomorphism classes: | 16 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $319$ | $285505$ | $150690496$ | $78486752025$ | $41426425940119$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $12$ | $540$ | $12384$ | $280468$ | $6436332$ | $148041870$ | $3404956644$ | $78311764708$ | $1801153569312$ | $41426495138700$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 16 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=14x^6+18x^5+20x^4+10x^3+2x^2+5x+7$
- $y^2=19x^6+6x^4+10x^3+12x^2+6x+7$
- $y^2=6x^6+13x^5+20x^4+10x^3+19x^2+22x+19$
- $y^2=13x^6+x^5+8x^4+19x^3+14x^2+12x+11$
- $y^2=19x^6+2x^5+14x^4+2x^3+19x^2+21x+20$
- $y^2=10x^6+20x^5+x^4+20x^3+5x^2+21x+20$
- $y^2=7x^6+10x^5+2x^4+19x^2+4x+7$
- $y^2=19x^6+17x^5+6x^4+19x^3+5x^2+17x+10$
- $y^2=19x^6+22x^5+8x^4+19x^3+6x+12$
- $y^2=14x^6+4x^5+4x^4+8x^3+7x^2+6x+14$
- $y^2=14x^6+3x^5+4x^4+21x^3+16x^2+19x+7$
- $y^2=7x^6+17x^5+17x^4+6x^3+2x^2+9x+22$
- $y^2=4x^6+18x^5+8x^4+6x^3+5x^2+11x+22$
- $y^2=19x^6+21x^5+x^4+14x^2+x+5$
- $y^2=15x^6+7x^5+3x^4+11x^3+17x^2+x+18$
- $y^2=10x^6+3x^5+10x^4+11x^3+18x^2+18x+11$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{23}$.
Endomorphism algebra over $\F_{23}$The endomorphism algebra of this simple isogeny class is 4.0.47025.1. |
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.m_cz | $2$ | (not in LMFDB) |