Invariants
Base field: | $\F_{157}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 44 x + 791 x^{2} - 6908 x^{3} + 24649 x^{4}$ |
Frobenius angles: | $\pm0.0579519561162$, $\pm0.219096909544$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.4090128.2 |
Galois group: | $D_{4}$ |
Jacobians: | $8$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $18489$ | $598914177$ | $14970283936308$ | $369150561411426729$ | $9099080042964659421249$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $114$ | $24296$ | $3868398$ | $607582036$ | $95389203714$ | $14976072525998$ | $2351243238973386$ | $369145193568094564$ | $57955795533886186854$ | $9099059900929105433816$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=47x^6+6x^5+84x^4+75x^3+131x^2+96x+156$
- $y^2=23x^6+64x^5+49x^4+24x^3+85x^2+33x+59$
- $y^2=81x^6+x^5+105x^4+135x^3+29x^2+130x+128$
- $y^2=138x^6+113x^5+53x^4+147x^3+88x^2+124x+52$
- $y^2=51x^6+75x^5+82x^4+138x^3+6x^2+25x+145$
- $y^2=156x^6+116x^5+53x^4+65x^3+7x^2+74x+7$
- $y^2=127x^6+137x^5+48x^4+111x^3+21x^2+56x+17$
- $y^2=139x^6+67x^5+5x^4+74x^3+23x^2+34x+124$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{157}$.
Endomorphism algebra over $\F_{157}$The endomorphism algebra of this simple isogeny class is 4.0.4090128.2. |
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 |
---|---|---|
2.157.bs_bel | $2$ | (not in LMFDB) |