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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 317900.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 317900.n1 | 317900n1 | \([0, -1, 0, -724908, 237802312]\) | \(-126100646224/605\) | \(-202120820000000\) | \([]\) | \(2115072\) | \(1.9460\) | \(\Gamma_0(N)\)-optimal |
| 317900.n2 | 317900n2 | \([0, -1, 0, -435908, 428542312]\) | \(-27419122384/221445125\) | \(-73981273140500000000\) | \([]\) | \(6345216\) | \(2.4953\) |
Rank
sage: E.rank()
The elliptic curves in class 317900.n have rank \(1\).
Complex multiplication
The elliptic curves in class 317900.n do not have complex multiplication.Modular form 317900.2.a.n
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
