Invariants
Base field: | $\F_{73}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 27 x + 317 x^{2} - 1971 x^{3} + 5329 x^{4}$ |
Frobenius angles: | $\pm0.0527273925472$, $\pm0.297649276576$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.37525.1 |
Galois group: | $D_{4}$ |
Jacobians: | $18$ |
Isomorphism classes: | 18 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $3649$ | $27896605$ | $151365223561$ | $806471462409525$ | $4297505155999078144$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $47$ | $5235$ | $389099$ | $28398643$ | $2073013382$ | $151333193355$ | $11047389441779$ | $806460057374083$ | $58871586928034927$ | $4297625834193221550$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 18 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=5x^6+22x^5+12x^4+59x^3+39x^2+11x+50$
- $y^2=65x^6+65x^5+50x^4+23x^3+67x^2+48x+37$
- $y^2=63x^6+22x^5+43x^4+29x^3+57x^2+17x+39$
- $y^2=13x^6+57x^5+30x^4+46x^3+43x^2+69x+34$
- $y^2=38x^6+45x^5+45x^4+30x^3+11x^2+11x+32$
- $y^2=28x^6+15x^5+67x^4+53x^3+10x^2+67x+10$
- $y^2=25x^6+5x^5+2x^4+65x^3+65x^2+2x+22$
- $y^2=46x^6+46x^5+9x^4+60x^3+27x^2+26x+34$
- $y^2=51x^6+67x^5+65x^4+42x^3+4x^2+57x+26$
- $y^2=33x^6+61x^5+44x^4+53x^3+60x^2+39x+68$
- $y^2=38x^6+17x^5+17x^4+44x^3+14x^2+21x+46$
- $y^2=58x^6+61x^5+35x^4+55x^3+38x^2+15x+42$
- $y^2=67x^5+24x^4+3x^3+37x^2+16x+68$
- $y^2=56x^6+52x^5+x^4+35x^3+38x^2+44x+22$
- $y^2=47x^6+50x^5+58x^4+7x^3+34x^2+51x+56$
- $y^2=40x^6+72x^5+46x^4+47x^3+55x^2+55x+62$
- $y^2=36x^6+39x^5+67x^4+4x^3+41x^2+27x+57$
- $y^2=66x^6+66x^5+23x^4+47x^3+69x^2+7x+56$
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 4.0.37525.1. |
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_mf | $2$ | (not in LMFDB) |