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SageMath
E = EllipticCurve("de1")
E.isogeny_class()
Elliptic curves in class 37440de
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37440.p2 | 37440de1 | \([0, 0, 0, 1075572, -254622448]\) | \(19441890357117957/15208161280000\) | \(-107641662225776640000\) | \([2]\) | \(983040\) | \(2.5318\) | \(\Gamma_0(N)\)-optimal |
| 37440.p1 | 37440de2 | \([0, 0, 0, -5068428, -2198584048]\) | \(2034416504287874043/882294347833600\) | \(6244780576999263436800\) | \([2]\) | \(1966080\) | \(2.8783\) |
Rank
sage: E.rank()
The elliptic curves in class 37440de have rank \(1\).
Complex multiplication
The elliptic curves in class 37440de do not have complex multiplication.Modular form 37440.2.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.
