Invariants
Base field: | $\F_{73}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 26 x + 305 x^{2} - 1898 x^{3} + 5329 x^{4}$ |
Frobenius angles: | $\pm0.105254807566$, $\pm0.304726056456$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.9614400.1 |
Galois group: | $D_{4}$ |
Jacobians: | $14$ |
Isomorphism classes: | 28 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $3711$ | $28051449$ | $151536473244$ | $806619668458041$ | $4297627396894974591$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $48$ | $5264$ | $389538$ | $28403860$ | $2073072348$ | $151333871078$ | $11047396945500$ | $806460130812964$ | $58871587521895794$ | $4297625837893859264$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 14 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=50x^6+16x^5+50x^4+50x^3+54x^2+26x+56$
- $y^2=5x^6+17x^5+40x^4+63x^3+36x^2+69x+24$
- $y^2=66x^6+x^5+16x^4+52x^3+63x^2+9x+43$
- $y^2=60x^6+35x^5+34x^4+49x^3+44x^2+15x+36$
- $y^2=44x^6+41x^5+68x^3+39x^2+20x+68$
- $y^2=26x^6+43x^5+13x^4+13x^3+19x^2+65x+29$
- $y^2=26x^6+25x^5+37x^4+40x^3+48x^2+23x+10$
- $y^2=21x^6+7x^5+67x^4+19x^2+57x+4$
- $y^2=51x^6+12x^5+14x^4+48x^3+47x^2+67x+65$
- $y^2=70x^6+47x^5+31x^4+31x^3+8x^2+48x+10$
- $y^2=53x^6+11x^5+19x^4+61x^3+59x^2+69x+33$
- $y^2=62x^6+72x^5+26x^4+12x^3+6x^2+61x+25$
- $y^2=59x^6+34x^5+64x^4+44x^3+8x^2+45x+51$
- $y^2=54x^6+26x^5+20x^4+72x^3+54x^2+55x+10$
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 4.0.9614400.1. |
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_lt | $2$ | (not in LMFDB) |