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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 226576n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 226576.u2 | 226576n1 | \([0, 1, 0, 7132424, -1420021548]\) | \(3449795831/2071552\) | \(-24095589495927054794752\) | \([2]\) | \(26542080\) | \(2.9840\) | \(\Gamma_0(N)\)-optimal |
| 226576.u1 | 226576n2 | \([0, 1, 0, -29119736, -11498122028]\) | \(234770924809/130960928\) | \(1523293048445638495305728\) | \([2]\) | \(53084160\) | \(3.3305\) |
Rank
sage: E.rank()
The elliptic curves in class 226576n have rank \(1\).
Complex multiplication
The elliptic curves in class 226576n do not have complex multiplication.Modular form 226576.2.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.
