Invariants
Base field: | $\F_{73}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 27 x + 320 x^{2} - 1971 x^{3} + 5329 x^{4}$ |
Frobenius angles: | $\pm0.0924528906443$, $\pm0.286344686183$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.291852.1 |
Galois group: | $D_{4}$ |
Jacobians: | $14$ |
Isomorphism classes: | 14 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $3652$ | $27930496$ | $151460141008$ | $806611385581056$ | $4297643689006581892$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $47$ | $5241$ | $389342$ | $28403569$ | $2073080207$ | $151333867086$ | $11047394837351$ | $806460096020833$ | $58871587243959470$ | $4297625837504144121$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 14 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=34x^6+69x^5+17x^4+58x^3+48x^2+36x+17$
- $y^2=44x^6+17x^5+42x^4+12x^3+30x^2+40x+36$
- $y^2=52x^6+57x^5+56x^4+x^3+2x^2+24x+62$
- $y^2=20x^6+46x^5+29x^4+45x^3+11x^2+64x+52$
- $y^2=29x^6+71x^5+7x^4+24x^3+61x^2+60x+29$
- $y^2=12x^6+37x^5+9x^4+39x^3+68x^2+63x+34$
- $y^2=22x^6+30x^5+61x^4+18x^3+62x^2+20x+50$
- $y^2=62x^6+47x^5+32x^4+28x^3+56x^2+7x+7$
- $y^2=30x^6+69x^5+59x^4+61x^3+32x^2+29x+10$
- $y^2=17x^6+71x^5+22x^4+69x^3+34x^2+9x+34$
- $y^2=46x^6+60x^5+60x^4+29x^3+28x^2+65x+9$
- $y^2=30x^6+26x^5+33x^4+70x^3+70x^2+17x+53$
- $y^2=9x^6+54x^5+9x^4+70x^3+58x^2+37x+70$
- $y^2=12x^6+3x^5+46x^4+34x^3+51x^2+49x+45$
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 4.0.291852.1. |
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_mi | $2$ | (not in LMFDB) |