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SageMath
E = EllipticCurve("dl1")
E.isogeny_class()
Elliptic curves in class 67600dl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
67600.p2 | 67600dl1 | \([0, 1, 0, -368, 2068]\) | \(4913\) | \(1124864000\) | \([2]\) | \(24576\) | \(0.45238\) | \(\Gamma_0(N)\)-optimal |
67600.p1 | 67600dl2 | \([0, 1, 0, -5568, 158068]\) | \(16974593\) | \(1124864000\) | \([2]\) | \(49152\) | \(0.79895\) |
Rank
sage: E.rank()
The elliptic curves in class 67600dl have rank \(2\).
Complex multiplication
The elliptic curves in class 67600dl do not have complex multiplication.Modular form 67600.2.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.