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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 40560v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 40560.cb1 | 40560v1 | \([0, 1, 0, -58231, -4833100]\) | \(621217777580032/74733890625\) | \(2627045723250000\) | \([2]\) | \(225792\) | \(1.6895\) | \(\Gamma_0(N)\)-optimal |
| 40560.cb2 | 40560v2 | \([0, 1, 0, 83924, -24621076]\) | \(116227003261808/533935546875\) | \(-300302437500000000\) | \([2]\) | \(451584\) | \(2.0360\) |
Rank
sage: E.rank()
The elliptic curves in class 40560v have rank \(1\).
Complex multiplication
The elliptic curves in class 40560v do not have complex multiplication.Modular form 40560.2.a.v
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 Cremona 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 Cremona labels.
