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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 726.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
726.c1 | 726c3 | \([1, 1, 0, -42594, 3365850]\) | \(4824238966273/66\) | \(116923026\) | \([2]\) | \(1920\) | \(1.1040\) | |
726.c2 | 726c2 | \([1, 1, 0, -2664, 51660]\) | \(1180932193/4356\) | \(7716919716\) | \([2, 2]\) | \(960\) | \(0.75742\) | |
726.c3 | 726c4 | \([1, 1, 0, -1454, 100302]\) | \(-192100033/2371842\) | \(-4201862785362\) | \([2]\) | \(1920\) | \(1.1040\) | |
726.c4 | 726c1 | \([1, 1, 0, -244, -128]\) | \(912673/528\) | \(935384208\) | \([2]\) | \(480\) | \(0.41085\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 726.c have rank \(0\).
Complex multiplication
The elliptic curves in class 726.c do not have complex multiplication.Modular form 726.2.a.c
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.