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SageMath
E = EllipticCurve("en1")
E.isogeny_class()
Elliptic curves in class 291312.en
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 291312.en1 | 291312en1 | \([0, 0, 0, -877404, -316028725]\) | \(265327034368/297381\) | \(83724826600786896\) | \([2]\) | \(3317760\) | \(2.1613\) | \(\Gamma_0(N)\)-optimal |
| 291312.en2 | 291312en2 | \([0, 0, 0, -656319, -479145238]\) | \(-6940769488/18000297\) | \(-81085032067962085632\) | \([2]\) | \(6635520\) | \(2.5078\) |
Rank
sage: E.rank()
The elliptic curves in class 291312.en have rank \(1\).
Complex multiplication
The elliptic curves in class 291312.en do not have complex multiplication.Modular form 291312.2.a.en
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
