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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 68970.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 68970.ba1 | 68970u1 | \([1, 0, 1, -2940424, 1686491222]\) | \(1587074323222816849/224665436160000\) | \(398008524749045760000\) | \([2]\) | \(3317760\) | \(2.6787\) | \(\Gamma_0(N)\)-optimal |
| 68970.ba2 | 68970u2 | \([1, 0, 1, 4803576, 9071169622]\) | \(6919293138571999151/24068144896012800\) | \(-42638186840125331980800\) | \([2]\) | \(6635520\) | \(3.0252\) |
Rank
sage: E.rank()
The elliptic curves in class 68970.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 68970.ba do not have complex multiplication.Modular form 68970.2.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.
