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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 2640.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2640.d1 | 2640d1 | \([0, -1, 0, -131, -534]\) | \(15657723904/49005\) | \(784080\) | \([2]\) | \(512\) | \(-0.0015979\) | \(\Gamma_0(N)\)-optimal |
2640.d2 | 2640d2 | \([0, -1, 0, -76, -1040]\) | \(-192143824/1804275\) | \(-461894400\) | \([2]\) | \(1024\) | \(0.34498\) |
Rank
sage: E.rank()
The elliptic curves in class 2640.d have rank \(0\).
Complex multiplication
The elliptic curves in class 2640.d do not have complex multiplication.Modular form 2640.2.a.d
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.