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SageMath
E = EllipticCurve("dn1")
E.isogeny_class()
Elliptic curves in class 162240.dn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162240.dn1 | 162240cy2 | \([0, -1, 0, -892545, -324154143]\) | \(497169541448/190125\) | \(30071097298944000\) | \([2]\) | \(2580480\) | \(2.1278\) | |
| 162240.dn2 | 162240cy1 | \([0, -1, 0, -47545, -6603143]\) | \(-601211584/609375\) | \(-12047715264000000\) | \([2]\) | \(1290240\) | \(1.7812\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 162240.dn have rank \(1\).
Complex multiplication
The elliptic curves in class 162240.dn do not have complex multiplication.Modular form 162240.2.a.dn
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
