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SageMath
E = EllipticCurve("de1")
E.isogeny_class()
Elliptic curves in class 59290.de
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 59290.de1 | 59290ej1 | \([1, 1, 1, -524840, 147527337]\) | \(-76711450249/851840\) | \(-177542520255013760\) | \([]\) | \(786240\) | \(2.1247\) | \(\Gamma_0(N)\)-optimal |
| 59290.de2 | 59290ej2 | \([1, 1, 1, 1757825, 766586085]\) | \(2882081488391/2883584000\) | \(-601003440466558976000\) | \([]\) | \(2358720\) | \(2.6740\) |
Rank
sage: E.rank()
The elliptic curves in class 59290.de have rank \(1\).
Complex multiplication
The elliptic curves in class 59290.de do not have complex multiplication.Modular form 59290.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
