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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 18480.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18480.bc1 | 18480cb2 | \([0, -1, 0, -428645, 2042286477]\) | \(-2126464142970105856/438611057788643355\) | \(-1796550892702283182080\) | \([]\) | \(1200000\) | \(2.7576\) | |
| 18480.bc2 | 18480cb1 | \([0, -1, 0, -143045, -24338643]\) | \(-79028701534867456/16987307596875\) | \(-69580011916800000\) | \([]\) | \(240000\) | \(1.9529\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 18480.bc have rank \(1\).
Complex multiplication
The elliptic curves in class 18480.bc do not have complex multiplication.Modular form 18480.2.a.bc
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
