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SageMath
E = EllipticCurve("eh1")
E.isogeny_class()
Elliptic curves in class 22050eh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
22050.do1 | 22050eh1 | \([1, -1, 1, -3380, 29747]\) | \(1092727/540\) | \(2109771562500\) | \([2]\) | \(36864\) | \(1.0579\) | \(\Gamma_0(N)\)-optimal |
22050.do2 | 22050eh2 | \([1, -1, 1, 12370, 218747]\) | \(53582633/36450\) | \(-142409580468750\) | \([2]\) | \(73728\) | \(1.4045\) |
Rank
sage: E.rank()
The elliptic curves in class 22050eh have rank \(0\).
Complex multiplication
The elliptic curves in class 22050eh do not have complex multiplication.Modular form 22050.2.a.eh
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.