Invariants
Base field: | $\F_{107}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 34 x + 490 x^{2} - 3638 x^{3} + 11449 x^{4}$ |
Frobenius angles: | $\pm0.0284553568954$, $\pm0.275837497585$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.143312.2 |
Galois group: | $D_{4}$ |
Jacobians: | $18$ |
Isomorphism classes: | 24 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $8268$ | $129080016$ | $1500437193372$ | $17181894627046656$ | $196713370851319014108$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $74$ | $11274$ | $1224806$ | $131079854$ | $14025391474$ | $1500727099194$ | $160578102357838$ | $17181861391591198$ | $1838459210391016250$ | $196715135731737170154$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 18 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=51x^6+93x^5+52x^4+x^3+65x^2+91x+19$
- $y^2=11x^6+106x^5+18x^4+26x^3+70x^2+78x+40$
- $y^2=105x^6+41x^5+77x^4+48x^3+90x^2+72x+59$
- $y^2=56x^6+26x^5+69x^4+37x^3+67x^2+43x+94$
- $y^2=3x^6+74x^5+86x^4+59x^3+28x^2+63x+2$
- $y^2=63x^6+67x^5+64x^4+16x^3+89x^2+100x+106$
- $y^2=45x^6+13x^5+23x^4+78x^3+46x^2+99x+4$
- $y^2=2x^6+13x^5+14x^4+68x^3+38x^2+21x+14$
- $y^2=2x^6+87x^5+71x^4+91x^3+33x^2+11x+54$
- $y^2=88x^6+12x^5+34x^4+21x^3+26x^2+39x+2$
- $y^2=52x^6+49x^5+45x^4+54x^3+70x^2+14x+74$
- $y^2=12x^6+48x^5+60x^4+35x^3+50x^2+47x+10$
- $y^2=62x^6+85x^5+72x^4+10x^3+61x^2+24x+84$
- $y^2=33x^6+61x^5+3x^4+62x^3+27x^2+81x+31$
- $y^2=79x^6+41x^5+79x^4+75x^3+57x^2+45x+6$
- $y^2=26x^6+81x^5+95x^4+92x^3+37x^2+57x+3$
- $y^2=5x^6+62x^5+39x^4+23x^3+25x^2+75x+56$
- $y^2=11x^6+14x^5+x^4+103x^3+63x^2+34x+24$
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 4.0.143312.2. |
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 |
---|---|---|
2.107.bi_sw | $2$ | (not in LMFDB) |