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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 212160.bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 212160.bl1 | 212160dx1 | \([0, -1, 0, -871681, -309383519]\) | \(279419703685750081/3666124800000\) | \(961052619571200000\) | \([2]\) | \(2949120\) | \(2.2583\) | \(\Gamma_0(N)\)-optimal |
| 212160.bl2 | 212160dx2 | \([0, -1, 0, -134401, -816779615]\) | \(-1024222994222401/1098922500000000\) | \(-288075939840000000000\) | \([2]\) | \(5898240\) | \(2.6048\) |
Rank
sage: E.rank()
The elliptic curves in class 212160.bl have rank \(1\).
Complex multiplication
The elliptic curves in class 212160.bl do not have complex multiplication.Modular form 212160.2.a.bl
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.
