Invariants
Base field: | $\F_{73}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 26 x + 300 x^{2} - 1898 x^{3} + 5329 x^{4}$ |
Frobenius angles: | $\pm0.0505498052565$, $\pm0.320643705385$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.5486400.1 |
Galois group: | $D_{4}$ |
Jacobians: | $12$ |
Isomorphism classes: | 24 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $3706$ | $27995124$ | $151384203754$ | $806407497435216$ | $4297433359296503866$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $48$ | $5254$ | $389148$ | $28396390$ | $2072978748$ | $151333019638$ | $11047390792080$ | $806460086634814$ | $58871587094183184$ | $4297625833079503414$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=36x^6+33x^5+17x^4+x^3+14x^2+52x+10$
- $y^2=38x^6+17x^5+7x^4+25x^3+19x^2+4x+43$
- $y^2=62x^6+27x^4+52x^3+69x^2+48x+60$
- $y^2=42x^6+31x^5+48x^4+44x^3+8x^2+20$
- $y^2=21x^6+51x^5+46x^4+56x^3+7x^2+58x+13$
- $y^2=33x^6+18x^5+14x^4+71x^3+45x^2+x+17$
- $y^2=66x^6+40x^5+47x^4+35x^3+30x^2+2x+59$
- $y^2=7x^6+67x^5+42x^4+23x^3+41x^2+7x+58$
- $y^2=42x^6+60x^5+40x^4+22x^3+13x^2+67x+1$
- $y^2=59x^6+11x^5+3x^4+33x^3+51x^2+58x+14$
- $y^2=12x^6+7x^5+20x^4+67x^3+9x^2+30x+53$
- $y^2=36x^6+57x^5+15x^4+47x^3+52x^2+44x+61$
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 4.0.5486400.1. |
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.ba_lo | $2$ | (not in LMFDB) |