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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 239904.db
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
239904.db1 | 239904db2 | \([0, 0, 0, -2572059, -36006082]\) | \(42852953779784/24786408969\) | \(1088427085204858495488\) | \([2]\) | \(8847360\) | \(2.7261\) | |
239904.db2 | 239904db1 | \([0, 0, 0, 642831, -4500160]\) | \(5352028359488/3098832471\) | \(-17009589802656959424\) | \([2]\) | \(4423680\) | \(2.3795\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 239904.db have rank \(1\).
Complex multiplication
The elliptic curves in class 239904.db do not have complex multiplication.Modular form 239904.2.a.db
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.