Invariants
Base field: | $\F_{73}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 27 x + 318 x^{2} - 1971 x^{3} + 5329 x^{4}$ |
Frobenius angles: | $\pm0.0678243041225$, $\pm0.294103344880$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.4081468.1 |
Galois group: | $D_{4}$ |
Jacobians: | $10$ |
Isomorphism classes: | 10 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $3650$ | $27907900$ | $151396860800$ | $806518216312000$ | $4297551893233813250$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $47$ | $5237$ | $389180$ | $28400289$ | $2073035927$ | $151333427234$ | $11047391458031$ | $806460074136961$ | $58871587089375020$ | $4297625835981020357$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 10 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=10x^6+33x^5+63x^4+7x^3+11x^2+9x+35$
- $y^2=6x^6+15x^5+34x^4+22x^3+67x^2+2x+28$
- $y^2=72x^6+60x^5+9x^4+61x^3+43x^2+40x+20$
- $y^2=71x^6+20x^5+4x^4+69x^3+16x^2+34x+9$
- $y^2=31x^6+17x^5+41x^4+61x^3+60x^2+21x+27$
- $y^2=58x^6+46x^5+18x^4+36x^3+16x^2+40x+13$
- $y^2=56x^6+15x^5+2x^4+22x^3+49x^2+11x+45$
- $y^2=25x^6+2x^5+8x^4+15x^3+26x^2+14x+56$
- $y^2=60x^6+42x^5+48x^4+22x^3+25x^2+67x+29$
- $y^2=35x^6+4x^5+12x^4+25x^3+18x^2+25x+19$
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 4.0.4081468.1. |
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.bb_mg | $2$ | (not in LMFDB) |