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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 200277ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 200277.t2 | 200277ba1 | \([1, -1, 0, -339918, 53995175]\) | \(1860867/539\) | \(1258115028295753089\) | \([2]\) | \(2297856\) | \(2.1792\) | \(\Gamma_0(N)\)-optimal |
| 200277.t1 | 200277ba2 | \([1, -1, 0, -4982703, 4281715196]\) | \(5861208627/847\) | \(1977037901607611997\) | \([2]\) | \(4595712\) | \(2.5258\) |
Rank
sage: E.rank()
The elliptic curves in class 200277ba have rank \(0\).
Complex multiplication
The elliptic curves in class 200277ba do not have complex multiplication.Modular form 200277.2.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 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.
