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SageMath
E = EllipticCurve("ds1")
E.isogeny_class()
Elliptic curves in class 285600.ds
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
285600.ds1 | 285600ds2 | \([0, 1, 0, -145808, 437388]\) | \(42852953779784/24786408969\) | \(198291271752000000\) | \([2]\) | \(2949120\) | \(2.0085\) | |
285600.ds2 | 285600ds1 | \([0, 1, 0, 36442, 72888]\) | \(5352028359488/3098832471\) | \(-3098832471000000\) | \([2]\) | \(1474560\) | \(1.6619\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 285600.ds have rank \(1\).
Complex multiplication
The elliptic curves in class 285600.ds do not have complex multiplication.Modular form 285600.2.a.ds
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.