Invariants
| Base field: | $\F_{73}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 26 x + 304 x^{2} - 1898 x^{3} + 5329 x^{4}$ |
| Frobenius angles: | $\pm0.0960067538857$, $\pm0.308228869049$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.9889088.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $22$ |
| Isomorphism classes: | 22 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $3710$ | $28040180$ | $151506015710$ | $806577460110800$ | $4297589667109673550$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $48$ | $5262$ | $389460$ | $28402374$ | $2073054148$ | $151333717854$ | $11047396090464$ | $806460128182206$ | $58871587518022080$ | $4297625837825484382$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 22 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=23x^6+18x^5+25x^4+58x^3+56x^2+62x+30$
- $y^2=14x^6+50x^5+39x^3+59x^2+45x+72$
- $y^2=51x^6+47x^5+4x^4+47x^3+53x^2+6x+58$
- $y^2=34x^6+17x^5+29x^4+28x^3+67x^2+38x+35$
- $y^2=8x^6+21x^5+38x^4+44x^3+32x^2+37x+9$
- $y^2=34x^6+66x^5+51x^4+40x^3+13x^2+32x+1$
- $y^2=29x^6+4x^5+68x^4+36x^3+21x^2+20x+51$
- $y^2=33x^6+50x^5+44x^4+68x^3+69x^2+59x+33$
- $y^2=50x^6+3x^5+22x^4+45x^3+18x^2+20x+22$
- $y^2=30x^6+41x^5+14x^4+50x^3+10x^2+40x+13$
- $y^2=49x^6+30x^5+54x^4+64x^3+35x^2+60x+14$
- $y^2=27x^6+72x^5+18x^4+62x^3+41x^2+27x+47$
- $y^2=5x^6+31x^5+65x^4+43x^3+x^2+70x+14$
- $y^2=21x^6+20x^5+72x^4+42x^3+48x^2+54x+30$
- $y^2=17x^6+12x^5+9x^4+69x^3+5x^2+55x+33$
- $y^2=45x^6+43x^5+59x^4+69x^3+20x^2+18x+65$
- $y^2=33x^6+22x^5+58x^4+60x^3+48x^2+61x+31$
- $y^2=59x^6+63x^5+30x^4+23x^3+61x^2+18x+10$
- $y^2=44x^6+21x^5+4x^4+30x^3+28x^2+29x+60$
- $y^2=34x^6+56x^5+34x^4+6x^3+65x^2+52x+11$
- $y^2=11x^6+54x^5+63x^4+38x^3+22x^2+13x+10$
- $y^2=61x^6+33x^5+31x^4+18x^3+4x^2+40x+20$
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 4.0.9889088.1. |
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_ls | $2$ | (not in LMFDB) |