Invariants
Base field: | $\F_{73}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 27 x + 325 x^{2} - 1971 x^{3} + 5329 x^{4}$ |
Frobenius angles: | $\pm0.146798730614$, $\pm0.260008220746$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.1516437.3 |
Galois group: | $D_{4}$ |
Jacobians: | $16$ |
Isomorphism classes: | 16 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $3657$ | $27987021$ | $151618375233$ | $806842334319381$ | $4297863386245838592$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $47$ | $5251$ | $389747$ | $28411699$ | $2073186182$ | $151334804491$ | $11047399528331$ | $806460085368643$ | $58871586733075055$ | $4297625831402083246$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 16 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=52x^6+48x^5+38x^4+10x^3+35x^2+40x+21$
- $y^2=30x^6+47x^4+25x^3+43x^2+22x+8$
- $y^2=37x^6+8x^5+65x^4+12x^3+26x^2+30x+28$
- $y^2=52x^6+12x^5+22x^4+38x^3+40x^2+14x+48$
- $y^2=42x^6+59x^5+41x^3+21x^2+28x+34$
- $y^2=62x^6+31x^5+71x^4+66x^3+11x^2+66x+19$
- $y^2=33x^6+38x^5+62x^4+63x^3+10x^2+43x+34$
- $y^2=55x^6+8x^5+40x^4+4x^3+63x^2+49x+56$
- $y^2=41x^6+29x^5+40x^4+44x^3+21x^2+42x+53$
- $y^2=39x^6+67x^5+51x^4+32x^3+16x^2+50x+24$
- $y^2=2x^6+41x^5+26x^4+40x^3+64x^2+67x+42$
- $y^2=62x^6+20x^4+40x^3+19x^2+68x$
- $y^2=59x^6+35x^5+26x^4+70x^3+38x^2+70x+57$
- $y^2=56x^6+35x^5+8x^4+8x^3+23x^2+16x+34$
- $y^2=36x^6+7x^5+55x^4+47x^3+5x^2+50x+9$
- $y^2=15x^6+43x^5+58x^4+60x^3+36x^2+37x+9$
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 4.0.1516437.3. |
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_mn | $2$ | (not in LMFDB) |