Invariants
Base field: | $\F_{73}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 26 x + 302 x^{2} - 1898 x^{3} + 5329 x^{4}$ |
Frobenius angles: | $\pm0.0758185551919$, $\pm0.314715919595$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.62192.1 |
Galois group: | $D_{4}$ |
Jacobians: | $36$ |
Isomorphism classes: | 48 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $3708$ | $28017648$ | $151445106108$ | $806492704644864$ | $4297512590945200188$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $48$ | $5258$ | $389304$ | $28399390$ | $2073016968$ | $151333385834$ | $11047393819104$ | $806460113714110$ | $58871587390903296$ | $4297625836420630538$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 36 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=17x^6+45x^5+24x^4+63x^3+54x^2+4x+62$
- $y^2=60x^6+45x^5+16x^4+29x^3+35x^2+11x+43$
- $y^2=51x^6+31x^5+5x^4+18x^3+29x^2+44x+48$
- $y^2=6x^6+33x^5+16x^4+54x^3+28x^2+62x+28$
- $y^2=35x^6+25x^5+67x^4+41x^3+21x^2+40x+13$
- $y^2=23x^6+17x^5+2x^4+33x^3+13x^2+34x+6$
- $y^2=29x^6+44x^5+16x^4+23x^3+42x^2+35x+2$
- $y^2=54x^6+62x^5+22x^4+12x^3+24x^2+69x+15$
- $y^2=24x^6+24x^5+65x^4+27x^3+56x^2+16x$
- $y^2=33x^6+25x^5+52x^4+48x^3+3x^2+19x+5$
- $y^2=26x^6+2x^5+70x^4+46x^3+70x^2+38$
- $y^2=16x^6+65x^5+60x^4+66x^3+47x^2+16x+65$
- $y^2=42x^6+68x^5+23x^4+36x^3+36x^2+47x+29$
- $y^2=69x^6+11x^5+14x^4+20x^3+15x^2+x+58$
- $y^2=29x^6+16x^5+29x^4+49x^3+42x^2+16x+21$
- $y^2=22x^6+8x^5+58x^4+14x^3+x^2+25x+47$
- $y^2=52x^6+48x^5+29x^4+32x^3+11x^2+39x+19$
- $y^2=22x^6+72x^5+37x^4+24x^3+2x^2+57x+31$
- $y^2=66x^6+37x^5+18x^4+55x^3+43x^2+4x+52$
- $y^2=56x^6+33x^5+62x^4+23x^3+58x^2+23x+16$
- and 16 more
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 4.0.62192.1. |
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.ba_lq | $2$ | (not in LMFDB) |