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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 238260s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
238260.s2 | 238260s1 | \([0, 1, 0, 13959, -701316]\) | \(399589376/517275\) | \(-389370529508400\) | \([2]\) | \(691200\) | \(1.4855\) | \(\Gamma_0(N)\)-optimal |
238260.s1 | 238260s2 | \([0, 1, 0, -85316, -6896076]\) | \(5702413264/1608255\) | \(19369413976999680\) | \([2]\) | \(1382400\) | \(1.8321\) |
Rank
sage: E.rank()
The elliptic curves in class 238260s have rank \(1\).
Complex multiplication
The elliptic curves in class 238260s do not have complex multiplication.Modular form 238260.2.a.s
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.