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SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 207025cj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
207025.cj2 | 207025cj1 | \([1, 1, 0, -28200, 1455875]\) | \(4913\) | \(504833697265625\) | \([2]\) | \(737280\) | \(1.5369\) | \(\Gamma_0(N)\)-optimal |
207025.cj1 | 207025cj2 | \([1, 1, 0, -426325, 106959000]\) | \(16974593\) | \(504833697265625\) | \([2]\) | \(1474560\) | \(1.8835\) |
Rank
sage: E.rank()
The elliptic curves in class 207025cj have rank \(0\).
Complex multiplication
The elliptic curves in class 207025cj do not have complex multiplication.Modular form 207025.2.a.cj
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.