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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 5850.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5850.p1 | 5850i3 | \([1, -1, 0, -103392, 12822016]\) | \(-10730978619193/6656\) | \(-75816000000\) | \([]\) | \(19440\) | \(1.4084\) | |
| 5850.p2 | 5850i2 | \([1, -1, 0, -1017, 25141]\) | \(-10218313/17576\) | \(-200201625000\) | \([]\) | \(6480\) | \(0.85911\) | |
| 5850.p3 | 5850i1 | \([1, -1, 0, 108, -734]\) | \(12167/26\) | \(-296156250\) | \([]\) | \(2160\) | \(0.30980\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5850.p have rank \(0\).
Complex multiplication
The elliptic curves in class 5850.p do not have complex multiplication.Modular form 5850.2.a.p
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
