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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 79560s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 79560.f1 | 79560s1 | \([0, 0, 0, -27802758, 56425604393]\) | \(203769809659907949070336/2016474841511325\) | \(23520162551388094800\) | \([2]\) | \(4055040\) | \(2.8770\) | \(\Gamma_0(N)\)-optimal |
| 79560.f2 | 79560s2 | \([0, 0, 0, -27139503, 59245632002]\) | \(-11845731628994222232016/1269935194601506875\) | \(-237000385757311619040000\) | \([2]\) | \(8110080\) | \(3.2236\) |
Rank
sage: E.rank()
The elliptic curves in class 79560s have rank \(2\).
Complex multiplication
The elliptic curves in class 79560s do not have complex multiplication.Modular form 79560.2.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.
