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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 194688cq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
194688.bw1 | 194688cq1 | \([0, 0, 0, -5070, -114244]\) | \(16000/3\) | \(2702395208448\) | \([2]\) | \(245760\) | \(1.1033\) | \(\Gamma_0(N)\)-optimal |
194688.bw2 | 194688cq2 | \([0, 0, 0, 10140, -667888]\) | \(4000/9\) | \(-259429940011008\) | \([2]\) | \(491520\) | \(1.4499\) |
Rank
sage: E.rank()
The elliptic curves in class 194688cq have rank \(0\).
Complex multiplication
The elliptic curves in class 194688cq do not have complex multiplication.Modular form 194688.2.a.cq
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.