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SageMath
E = EllipticCurve("dn1")
E.isogeny_class()
Elliptic curves in class 162450dn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162450.r2 | 162450dn1 | \([1, -1, 0, -118265292, -497275342884]\) | \(-341370886042369/1817528220\) | \(-973980636262482293437500\) | \([2]\) | \(38707200\) | \(3.4477\) | \(\Gamma_0(N)\)-optimal |
| 162450.r1 | 162450dn2 | \([1, -1, 0, -1894656042, -31742212244634]\) | \(1403607530712116449/39475350\) | \(21154129045481439843750\) | \([2]\) | \(77414400\) | \(3.7943\) |
Rank
sage: E.rank()
The elliptic curves in class 162450dn have rank \(1\).
Complex multiplication
The elliptic curves in class 162450dn do not have complex multiplication.Modular form 162450.2.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 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.
