Invariants
Base field: | $\F_{113}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 35 x + 531 x^{2} - 3955 x^{3} + 12769 x^{4}$ |
Frobenius angles: | $\pm0.160388096429$, $\pm0.219985207361$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.483725.1 |
Galois group: | $D_{4}$ |
Jacobians: | $8$ |
Isomorphism classes: | 8 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $9311$ | $160996501$ | $2083419015479$ | $26590104987836021$ | $339465560665668705136$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $79$ | $12607$ | $1443913$ | $163082091$ | $18424830594$ | $2081956165183$ | $235260572634733$ | $26584441896834483$ | $3004041935136908059$ | $339456738950587721022$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=89x^6+50x^5+103x^4+98x^3+79x^2+6x+80$
- $y^2=19x^6+16x^5+103x^4+34x^3+101x^2+54x+36$
- $y^2=101x^6+71x^5+23x^4+49x^3+81x^2+44x+71$
- $y^2=43x^6+57x^5+91x^4+71x^3+94x^2+94x+68$
- $y^2=30x^6+110x^5+67x^4+110x^3+8x^2+35x+44$
- $y^2=66x^6+104x^5+105x^4+12x^3+4x^2+10x$
- $y^2=58x^6+94x^5+82x^4+59x^3+64x^2+100x+71$
- $y^2=108x^6+52x^5+8x^4+89x^3+18x^2+87x+21$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{113}$.
Endomorphism algebra over $\F_{113}$The endomorphism algebra of this simple isogeny class is 4.0.483725.1. |
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 |
---|---|---|
2.113.bj_ul | $2$ | (not in LMFDB) |