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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 242760a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
242760.a1 | 242760a1 | \([0, -1, 0, -183951, 30416796]\) | \(8757210428192768/3859475445\) | \(303385645780560\) | \([2]\) | \(1474560\) | \(1.7377\) | \(\Gamma_0(N)\)-optimal |
242760.a2 | 242760a2 | \([0, -1, 0, -154796, 40352820]\) | \(-326151207424208/369125632575\) | \(-464259643607289600\) | \([2]\) | \(2949120\) | \(2.0843\) |
Rank
sage: E.rank()
The elliptic curves in class 242760a have rank \(1\).
Complex multiplication
The elliptic curves in class 242760a do not have complex multiplication.Modular form 242760.2.a.a
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.