Invariants
Base field: | $\F_{73}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 27 x + 327 x^{2} - 1971 x^{3} + 5329 x^{4}$ |
Frobenius angles: | $\pm0.173277117652$, $\pm0.242024654440$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.271525.1 |
Galois group: | $D_{4}$ |
Jacobians: | $11$ |
Isomorphism classes: | 11 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $3659$ | $28009645$ | $151681682531$ | $806933924203525$ | $4297947348358642544$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $47$ | $5255$ | $389909$ | $28414923$ | $2073226682$ | $151335114815$ | $11047399925609$ | $806460056107603$ | $58871586206922707$ | $4297625825906699150$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 11 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=22x^6+35x^5+49x^4+10x^3+66x^2+44x+14$
- $y^2=28x^6+64x^5+37x^4+72x^3+13x^2+42x+63$
- $y^2=50x^6+23x^5+38x^4+9x^3+8x^2+67x+6$
- $y^2=35x^6+39x^5+18x^4+72x^3+51x^2+41x+5$
- $y^2=52x^6+26x^5+50x^4+34x^3+70x^2+19x+47$
- $y^2=71x^6+43x^5+46x^4+8x^3+54x^2+13x+51$
- $y^2=61x^6+7x^5+55x^4+42x^3+14x^2+28x+52$
- $y^2=8x^6+24x^5+59x^4+34x^3+44x^2+14x+48$
- $y^2=29x^6+18x^5+48x^4+50x^3+11$
- $y^2=13x^6+47x^5+69x^4+6x^3+x^2+41x+15$
- $y^2=69x^6+14x^5+49x^4+13x^3+48x^2+66x+11$
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 4.0.271525.1. |
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_mp | $2$ | (not in LMFDB) |