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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 277350.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
277350.ba1 | 277350ba2 | \([1, 1, 0, -319915, 51433525]\) | \(4582567781/1198152\) | \(946744222485681000\) | \([2]\) | \(5677056\) | \(2.1582\) | |
277350.ba2 | 277350ba1 | \([1, 1, 0, 49885, 5208525]\) | \(17373979/24768\) | \(-19570939999704000\) | \([2]\) | \(2838528\) | \(1.8116\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 277350.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 277350.ba do not have complex multiplication.Modular form 277350.2.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.