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SageMath
E = EllipticCurve("dq1")
E.isogeny_class()
Elliptic curves in class 258570.dq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
258570.dq1 | 258570dq1 | \([1, -1, 1, -465458, -69969103]\) | \(3169397364769/1231093760\) | \(4331903487206031360\) | \([2]\) | \(4128768\) | \(2.2749\) | \(\Gamma_0(N)\)-optimal |
258570.dq2 | 258570dq2 | \([1, -1, 1, 1481422, -504512719]\) | \(102181603702751/90336313600\) | \(-317870339871739449600\) | \([2]\) | \(8257536\) | \(2.6215\) |
Rank
sage: E.rank()
The elliptic curves in class 258570.dq have rank \(1\).
Complex multiplication
The elliptic curves in class 258570.dq do not have complex multiplication.Modular form 258570.2.a.dq
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.