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SageMath
E = EllipticCurve("ed1")
E.isogeny_class()
Elliptic curves in class 35280ed
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35280.cg1 | 35280ed1 | \([0, 0, 0, -2163, -14798]\) | \(1092727/540\) | \(553063956480\) | \([2]\) | \(36864\) | \(0.94632\) | \(\Gamma_0(N)\)-optimal |
| 35280.cg2 | 35280ed2 | \([0, 0, 0, 7917, -113582]\) | \(53582633/36450\) | \(-37331817062400\) | \([2]\) | \(73728\) | \(1.2929\) |
Rank
sage: E.rank()
The elliptic curves in class 35280ed have rank \(0\).
Complex multiplication
The elliptic curves in class 35280ed do not have complex multiplication.Modular form 35280.2.a.ed
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.
