Invariants
Base field: | $\F_{73}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 31 x + 385 x^{2} - 2263 x^{3} + 5329 x^{4}$ |
Frobenius angles: | $\pm0.0748266886772$, $\pm0.181589986389$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.33725.1 |
Galois group: | $D_{4}$ |
Jacobians: | $2$ |
Isomorphism classes: | 2 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $3421$ | $27398789$ | $151033349269$ | $806479216997861$ | $4297734053417660416$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $43$ | $5139$ | $388243$ | $28398915$ | $2073123798$ | $151334849523$ | $11047403393755$ | $806460117614979$ | $58871586761053939$ | $4297625829147519214$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 2 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=40x^6+17x^5+37x^4+10x^3+37x^2+53x+14$
- $y^2=68x^6+45x^5+31x^4+3x^3+12x^2+24x+56$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{73}$.
Endomorphism algebra over $\F_{73}$The endomorphism algebra of this simple isogeny class is 4.0.33725.1. |
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 |
---|---|---|
2.73.bf_ov | $2$ | (not in LMFDB) |