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SageMath
E = EllipticCurve("dl1")
E.isogeny_class()
Elliptic curves in class 54080dl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54080.v2 | 54080dl1 | \([0, 1, 0, -20505, -886937]\) | \(21952/5\) | \(217180147159040\) | \([2]\) | \(259584\) | \(1.4635\) | \(\Gamma_0(N)\)-optimal |
54080.v1 | 54080dl2 | \([0, 1, 0, -108385, 12945375]\) | \(405224/25\) | \(8687205886361600\) | \([2]\) | \(519168\) | \(1.8101\) |
Rank
sage: E.rank()
The elliptic curves in class 54080dl have rank \(0\).
Complex multiplication
The elliptic curves in class 54080dl do not have complex multiplication.Modular form 54080.2.a.dl
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.