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SageMath
E = EllipticCurve("de1")
E.isogeny_class()
Elliptic curves in class 94640de
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 94640.m2 | 94640de1 | \([0, 1, 0, -16280, -242540]\) | \(24137569/12740\) | \(251877567119360\) | \([2]\) | \(258048\) | \(1.4549\) | \(\Gamma_0(N)\)-optimal |
| 94640.m1 | 94640de2 | \([0, 1, 0, -205560, -35902892]\) | \(48587168449/59150\) | \(1169431561625600\) | \([2]\) | \(516096\) | \(1.8015\) |
Rank
sage: E.rank()
The elliptic curves in class 94640de have rank \(0\).
Complex multiplication
The elliptic curves in class 94640de do not have complex multiplication.Modular form 94640.2.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.
