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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 6270.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6270.g1 | 6270h2 | \([1, 0, 1, -4105679, 3201688802]\) | \(7653825103704685955596009/4342288500000\) | \(4342288500000\) | \([2]\) | \(107520\) | \(2.1862\) | |
6270.g2 | 6270h1 | \([1, 0, 1, -256559, 50029346]\) | \(-1867596456486858577129/1407493853568000\) | \(-1407493853568000\) | \([2]\) | \(53760\) | \(1.8396\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6270.g have rank \(1\).
Complex multiplication
The elliptic curves in class 6270.g do not have complex multiplication.Modular form 6270.2.a.g
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.