Invariants
Base field: | $\F_{107}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 36 x + 536 x^{2} - 3852 x^{3} + 11449 x^{4}$ |
Frobenius angles: | $\pm0.112288198128$, $\pm0.203926913540$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.499968.5 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $8098$ | $128547652$ | $1500335061106$ | $17183896870412304$ | $196719088775649102178$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $72$ | $11226$ | $1224720$ | $131095126$ | $14025799152$ | $1500733493898$ | $160578173201112$ | $17181861942027934$ | $1838459212773454152$ | $196715135727105319866$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=21x^6+69x^5+63x^4+80x^3+69x^2+22x+51$
- $y^2=105x^6+12x^5+19x^4+80x^3+75x^2+91x+61$
- $y^2=65x^6+76x^5+67x^4+78x^3+83x^2+41x+68$
- $y^2=46x^6+91x^5+62x^4+35x^3+72x^2+19x+4$
- $y^2=12x^6+41x^5+66x^4+34x^3+71x^2+68x+98$
- $y^2=106x^6+103x^5+60x^4+72x^3+89x^2+61x+98$
- $y^2=85x^6+49x^5+89x^4+54x^3+103x^2+19x+46$
- $y^2=66x^6+63x^5+43x^4+46x^3+94x^2+61x+97$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{107}$.
Endomorphism algebra over $\F_{107}$The endomorphism algebra of this simple isogeny class is 4.0.499968.5. |
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 |
---|---|---|
2.107.bk_uq | $2$ | (not in LMFDB) |