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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 65520n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 65520.g1 | 65520n1 | \([0, 0, 0, -24723, -74142]\) | \(2238719766084/1292374265\) | \(964752219325440\) | \([2]\) | \(221184\) | \(1.5648\) | \(\Gamma_0(N)\)-optimal |
| 65520.g2 | 65520n2 | \([0, 0, 0, 98757, -592758]\) | \(71346044015118/41389887175\) | \(-61794770433177600\) | \([2]\) | \(442368\) | \(1.9113\) |
Rank
sage: E.rank()
The elliptic curves in class 65520n have rank \(0\).
Complex multiplication
The elliptic curves in class 65520n do not have complex multiplication.Modular form 65520.2.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 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.
