Invariants
Base field: | $\F_{73}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 27 x + 323 x^{2} - 1971 x^{3} + 5329 x^{4}$ |
Frobenius angles: | $\pm0.124803810750$, $\pm0.272272309487$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.3128013.1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $3655$ | $27964405$ | $151555075735$ | $806750293259925$ | $4297777185989508400$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $47$ | $5247$ | $389585$ | $28408459$ | $2073144602$ | $151334457279$ | $11047398290381$ | $806460100561651$ | $58871587082387555$ | $4297625835323421582$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 18 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=53x^6+3x^5+60x^4+56x^3+23x^2+59x+72$
- $y^2=5x^6+58x^5+35x^4+49x^3+70x^2+55x$
- $y^2=52x^6+20x^5+17x^4+53x^3+36x^2+16x+22$
- $y^2=x^6+27x^5+65x^4+8x^3+46x^2+3x+26$
- $y^2=7x^6+58x^5+43x^4+25x^3+9x^2+51x+43$
- $y^2=49x^5+2x^4+67x^3+48x^2+11x+37$
- $y^2=60x^6+64x^5+30x^4+63x^3+48x^2+8x+14$
- $y^2=55x^6+37x^5+44x^4+39x^3+17x^2+12x+45$
- $y^2=20x^6+38x^5+7x^4+4x^3+64x^2+9x+37$
- $y^2=31x^6+55x^5+27x^4+47x^3+66x^2+9x+23$
- $y^2=40x^6+32x^5+52x^4+58x^3+68x^2+62x+13$
- $y^2=29x^6+46x^5+14x^4+25x^3+41x^2+47x+62$
- $y^2=5x^6+53x^5+60x^4+16x^3+65x^2+41x+59$
- $y^2=51x^6+19x^5+17x^4+3x^3+45x^2+57x+34$
- $y^2=12x^6+39x^5+29x^4+23x^3+41x^2+65x+65$
- $y^2=2x^6+50x^5+70x^4+39x^3+15x^2+58x+29$
- $y^2=6x^6+42x^5+37x^4+34x^3+7x^2+25x+20$
- $y^2=47x^6+2x^5+29x^4+11x^2+70x+13$
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 4.0.3128013.1. |
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_ml | $2$ | (not in LMFDB) |