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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 350064co
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 350064.co1 | 350064co1 | \([0, 0, 0, -5681883, 4464288650]\) | \(6793805286030262681/1048227429629952\) | \(3129990333236162592768\) | \([2]\) | \(28901376\) | \(2.8480\) | \(\Gamma_0(N)\)-optimal |
| 350064.co2 | 350064co2 | \([0, 0, 0, 9893157, 24633965450]\) | \(35862531227445945959/108547797844556928\) | \(-324121987599081474097152\) | \([2]\) | \(57802752\) | \(3.1946\) |
Rank
sage: E.rank()
The elliptic curves in class 350064co have rank \(1\).
Complex multiplication
The elliptic curves in class 350064co do not have complex multiplication.Modular form 350064.2.a.co
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.
