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SageMath
E = EllipticCurve("de1")
E.isogeny_class()
Elliptic curves in class 286110de
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 286110.de2 | 286110de1 | \([1, -1, 0, -520254, 123691860]\) | \(885012508801/137332800\) | \(2416547473317172800\) | \([2]\) | \(5308416\) | \(2.2507\) | \(\Gamma_0(N)\)-optimal |
| 286110.de1 | 286110de2 | \([1, -1, 0, -2288934, -1212369012]\) | \(75370704203521/7497765000\) | \(131932830804264765000\) | \([2]\) | \(10616832\) | \(2.5972\) |
Rank
sage: E.rank()
The elliptic curves in class 286110de have rank \(0\).
Complex multiplication
The elliptic curves in class 286110de do not have complex multiplication.Modular form 286110.2.a.de
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.
