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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 7200.by
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7200.by1 | 7200y1 | \([0, 0, 0, -121125, -16225000]\) | \(2156689088/81\) | \(7381125000000\) | \([2]\) | \(30720\) | \(1.5555\) | \(\Gamma_0(N)\)-optimal |
| 7200.by2 | 7200y2 | \([0, 0, 0, -115500, -17800000]\) | \(-29218112/6561\) | \(-38263752000000000\) | \([2]\) | \(61440\) | \(1.9021\) |
Rank
sage: E.rank()
The elliptic curves in class 7200.by have rank \(1\).
Complex multiplication
The elliptic curves in class 7200.by do not have complex multiplication.Modular form 7200.2.a.by
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
