Invariants
Base field: | $\F_{73}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 28 x + 336 x^{2} - 2044 x^{3} + 5329 x^{4}$ |
Frobenius angles: | $\pm0.0872906235122$, $\pm0.263736764141$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.1956096.1 |
Galois group: | $D_{4}$ |
Jacobians: | $12$ |
Isomorphism classes: | 12 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $3594$ | $27810372$ | $151388627994$ | $806620150116624$ | $4297690205981945274$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $46$ | $5218$ | $389158$ | $28403878$ | $2073102646$ | $151334085058$ | $11047394905054$ | $806460071590846$ | $58871586899941774$ | $4297625835257832418$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=31x^6+42x^5+50x^4+47x^3+27x^2+14x+10$
- $y^2=5x^6+10x^5+47x^4+2x^3+54x^2+58x+10$
- $y^2=13x^6+37x^5+53x^4+10x^3+14x^2+59x+16$
- $y^2=68x^6+18x^5+43x^4+19x^3+26x^2+42x+8$
- $y^2=60x^6+25x^5+10x^4+21x^3+63x^2+42x+33$
- $y^2=65x^6+22x^5+38x^4+58x^3+26x^2+46x+7$
- $y^2=17x^6+x^5+59x^4+51x^3+57x^2+62x+5$
- $y^2=56x^6+5x^5+67x^4+4x^3+23x^2+42x+34$
- $y^2=60x^6+66x^5+58x^4+16x^3+30x^2+72x+70$
- $y^2=20x^6+13x^5+47x^4+21x^3+29x^2+64x+3$
- $y^2=68x^6+22x^5+39x^4+39x^3+24x^2+55x+35$
- $y^2=37x^6+14x^5+4x^4+34x^3+61x^2+71x$
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 4.0.1956096.1. |
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.bc_my | $2$ | (not in LMFDB) |