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SageMath
E = EllipticCurve("ex1")
E.isogeny_class()
Elliptic curves in class 35280ex
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35280.dz1 | 35280ex1 | \([0, 0, 0, -929187, 344749986]\) | \(-5154200289/20\) | \(-344272070983680\) | \([]\) | \(282240\) | \(2.0026\) | \(\Gamma_0(N)\)-optimal |
| 35280.dz2 | 35280ex2 | \([0, 0, 0, 6479613, -3271040766]\) | \(1747829720511/1280000000\) | \(-22033412542955520000000\) | \([]\) | \(1975680\) | \(2.9755\) |
Rank
sage: E.rank()
The elliptic curves in class 35280ex have rank \(0\).
Complex multiplication
The elliptic curves in class 35280ex do not have complex multiplication.Modular form 35280.2.a.ex
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
