Show commands:
SageMath
E = EllipticCurve("fq1")
E.isogeny_class()
Elliptic curves in class 259920.fq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
259920.fq1 | 259920fq1 | \([0, 0, 0, -1872507, 1135617194]\) | \(-14317849/2700\) | \(-136924148259226828800\) | \([]\) | \(9455616\) | \(2.5879\) | \(\Gamma_0(N)\)-optimal |
259920.fq2 | 259920fq2 | \([0, 0, 0, 12942933, -5563924774]\) | \(4728305591/3000000\) | \(-152137942510252032000000\) | \([]\) | \(28366848\) | \(3.1373\) |
Rank
sage: E.rank()
The elliptic curves in class 259920.fq have rank \(0\).
Complex multiplication
The elliptic curves in class 259920.fq do not have complex multiplication.Modular form 259920.2.a.fq
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.