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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 20070.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20070.ba1 | 20070w1 | \([1, -1, 1, -14528, 661987]\) | \(17227485284283/456704000\) | \(8989304832000\) | \([2]\) | \(74592\) | \(1.2667\) | \(\Gamma_0(N)\)-optimal |
| 20070.ba2 | 20070w2 | \([1, -1, 1, 2752, 2127331]\) | \(117145509957/99458000000\) | \(-1957631814000000\) | \([2]\) | \(149184\) | \(1.6132\) |
Rank
sage: E.rank()
The elliptic curves in class 20070.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 20070.ba do not have complex multiplication.Modular form 20070.2.a.ba
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.
