Invariants
Base field: | $\F_{107}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 35 x + 513 x^{2} - 3745 x^{3} + 11449 x^{4}$ |
Frobenius angles: | $\pm0.0698121762543$, $\pm0.246087952504$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.3556589.1 |
Galois group: | $D_{4}$ |
Jacobians: | $15$ |
Isomorphism classes: | 15 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $8183$ | $128824969$ | $1500430027481$ | $17182940904080861$ | $196716107706164708368$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $73$ | $11251$ | $1224799$ | $131087835$ | $14025586608$ | $1500729914647$ | $160578130432429$ | $17181861585333699$ | $1838459211366428863$ | $196715135741871505686$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 15 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=11x^5+76x^4+45x^3+101x^2+38x+45$
- $y^2=32x^6+55x^5+45x^4+40x^3+57x^2+93x+46$
- $y^2=94x^6+63x^5+13x^4+55x^3+105x^2+12x+93$
- $y^2=28x^6+50x^5+8x^4+17x^3+36x^2+52x+69$
- $y^2=19x^6+67x^5+98x^4+47x^3+67x^2+71x+95$
- $y^2=61x^6+98x^5+80x^4+34x^3+68x^2+81x+57$
- $y^2=103x^6+82x^5+61x^4+77x^3+22x^2+50x+14$
- $y^2=34x^6+34x^5+2x^4+10x^3+18x^2+98x+46$
- $y^2=91x^6+75x^5+10x^4+82x^3+11x^2+93x+59$
- $y^2=45x^6+24x^5+15x^4+58x^3+13x^2+14x+92$
- $y^2=81x^6+86x^5+24x^4+98x^3+20x^2+53x+50$
- $y^2=56x^6+83x^5+3x^4+19x^3+46x^2+44x+29$
- $y^2=73x^6+68x^5+85x^4+65x^3+27x^2+91x+25$
- $y^2=76x^6+76x^5+8x^4+68x^3+23x^2+101x+38$
- $y^2=58x^6+56x^5+5x^4+66x^3+62x^2+47x+46$
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 4.0.3556589.1. |
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 |
---|---|---|
2.107.bj_tt | $2$ | (not in LMFDB) |