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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 58835e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 58835.j2 | 58835e1 | \([1, -1, 0, -110, -25]\) | \(2146689/1225\) | \(84428225\) | \([2]\) | \(10240\) | \(0.21074\) | \(\Gamma_0(N)\)-optimal |
| 58835.j1 | 58835e2 | \([1, -1, 0, -1135, 14940]\) | \(2347334289/12005\) | \(827396605\) | \([2]\) | \(20480\) | \(0.55731\) |
Rank
sage: E.rank()
The elliptic curves in class 58835e have rank \(0\).
Complex multiplication
The elliptic curves in class 58835e do not have complex multiplication.Modular form 58835.2.a.e
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.
