Invariants
Base field: | $\F_{73}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 27 x + 321 x^{2} - 1971 x^{3} + 5329 x^{4}$ |
Frobenius angles: | $\pm0.103502055686$, $\pm0.282046802349$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.4390861.1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $3653$ | $27941797$ | $151491783989$ | $806657800962949$ | $4297688747553314048$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $47$ | $5243$ | $389423$ | $28405203$ | $2073101942$ | $151334073083$ | $11047396202687$ | $806460101251171$ | $58871587240781759$ | $4297625837328599918$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 14 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=65x^6+25x^5+52x^4+18x^3+48x^2+50x+45$
- $y^2=44x^6+2x^5+14x^4+71x^3+44x^2+5x+32$
- $y^2=23x^6+2x^5+19x^4+53x^3+32x^2+23x+15$
- $y^2=15x^6+15x^5+40x^4+31x^3+57x^2+11x+61$
- $y^2=59x^6+58x^5+17x^4+43x^3+53x^2+58x+43$
- $y^2=47x^6+46x^5+55x^4+48x^3+52x^2+59x+29$
- $y^2=34x^6+25x^5+41x^4+9x^3+35x^2+12x+30$
- $y^2=19x^6+28x^5+50x^4+64x^3+39x^2+29x+53$
- $y^2=55x^6+54x^5+x^4+56x^3+63x^2+53x+20$
- $y^2=50x^6+67x^5+5x^4+18x^3+21x^2+34x+3$
- $y^2=53x^6+39x^5+12x^4+46x^3+43x^2+25x+21$
- $y^2=28x^6+13x^5+51x^4+34x^3+34x^2+60x+28$
- $y^2=60x^6+5x^5+17x^4+10x^3+72x^2+10x+17$
- $y^2=29x^6+65x^5+19x^4+63x^3+2x^2+35x+40$
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 4.0.4390861.1. |
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_mj | $2$ | (not in LMFDB) |