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SageMath
E = EllipticCurve("de1")
E.isogeny_class()
Elliptic curves in class 162450de
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162450.e2 | 162450de1 | \([1, -1, 0, -1692, 27463216]\) | \(-1/608\) | \(-325816248865500000\) | \([]\) | \(1728000\) | \(2.0393\) | \(\Gamma_0(N)\)-optimal |
| 162450.e1 | 162450de2 | \([1, -1, 0, -5687442, -5777687534]\) | \(-37966934881/4952198\) | \(-2653793710525051593750\) | \([]\) | \(8640000\) | \(2.8440\) |
Rank
sage: E.rank()
The elliptic curves in class 162450de have rank \(1\).
Complex multiplication
The elliptic curves in class 162450de do not have complex multiplication.Modular form 162450.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
