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SageMath
E = EllipticCurve("cf1")
E.isogeny_class()
Elliptic curves in class 20286cf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
20286.bs2 | 20286cf1 | \([1, -1, 1, -3611, 389575]\) | \(-60698457/725788\) | \(-62248021428348\) | \([2]\) | \(73728\) | \(1.3287\) | \(\Gamma_0(N)\)-optimal |
20286.bs1 | 20286cf2 | \([1, -1, 1, -105041, 13088611]\) | \(1494447319737/5411854\) | \(464153724998334\) | \([2]\) | \(147456\) | \(1.6753\) |
Rank
sage: E.rank()
The elliptic curves in class 20286cf have rank \(0\).
Complex multiplication
The elliptic curves in class 20286cf do not have complex multiplication.Modular form 20286.2.a.cf
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.