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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 2280.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2280.g1 | 2280d2 | \([0, 1, 0, -360, -2592]\) | \(5052857764/346275\) | \(354585600\) | \([2]\) | \(768\) | \(0.38884\) | |
2280.g2 | 2280d1 | \([0, 1, 0, 20, -160]\) | \(3286064/48735\) | \(-12476160\) | \([2]\) | \(384\) | \(0.042265\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2280.g have rank \(1\).
Complex multiplication
The elliptic curves in class 2280.g do not have complex multiplication.Modular form 2280.2.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.