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SageMath
sage: E = EllipticCurve("j1")
sage: E.isogeny_class()
Elliptic curves in class 690.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
690.j1 | 690j2 | [1, 0, 0, -3925, -94975] | [2] | 480 | |
690.j2 | 690j1 | [1, 0, 0, -245, -1503] | [2] | 240 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 690.j have rank \(0\).
Complex multiplication
The elliptic curves in class 690.j do not have complex multiplication.Modular form 690.2.a.j
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.