Invariants
Base field: | $\F_{37}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 18 x + 149 x^{2} - 666 x^{3} + 1369 x^{4}$ |
Frobenius angles: | $\pm0.109754015015$, $\pm0.319010597563$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.1023552.2 |
Galois group: | $D_{4}$ |
Jacobians: | $4$ |
Isomorphism classes: | 4 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $835$ | $1839505$ | $2576666380$ | $3514824981225$ | $4808420985598675$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $20$ | $1344$ | $50870$ | $1875412$ | $69341600$ | $2565677166$ | $94931878880$ | $3512483541028$ | $129961783534430$ | $4808584619325264$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 4 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=35x^6+24x^5+30x^4+21x^3+x^2+19x+13$
- $y^2=23x^6+25x^5+18x^4+8x^3+25x^2+31x+6$
- $y^2=19x^6+30x^5+35x^4+13x^3+7x^2+34x+32$
- $y^2=22x^6+11x^5+7x^4+6x^3+10x^2+2x+8$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{37}$.
Endomorphism algebra over $\F_{37}$The endomorphism algebra of this simple isogeny class is 4.0.1023552.2. |
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 |
---|---|---|
2.37.s_ft | $2$ | (not in LMFDB) |