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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 164560s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 164560.y2 | 164560s1 | \([0, -1, 0, 772424, -81373840]\) | \(7023836099951/4456448000\) | \(-32337385370943488000\) | \([]\) | \(2903040\) | \(2.4326\) | \(\Gamma_0(N)\)-optimal |
| 164560.y1 | 164560s2 | \([0, -1, 0, -12857016, -18312112784]\) | \(-32391289681150609/1228250000000\) | \(-8912567493632000000000\) | \([]\) | \(8709120\) | \(2.9819\) |
Rank
sage: E.rank()
The elliptic curves in class 164560s have rank \(0\).
Complex multiplication
The elliptic curves in class 164560s do not have complex multiplication.Modular form 164560.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
