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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 399424.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 399424.e1 | 399424e2 | \([0, 1, 0, -3603137, 2254653247]\) | \(81182737/12482\) | \(795401943728291053568\) | \([2]\) | \(14376960\) | \(2.7340\) | |
| 399424.e2 | 399424e1 | \([0, 1, 0, 391103, 194424255]\) | \(103823/316\) | \(-20136758069070659584\) | \([2]\) | \(7188480\) | \(2.3874\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 399424.e have rank \(1\).
Complex multiplication
The elliptic curves in class 399424.e do not have complex multiplication.Modular form 399424.2.a.e
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.
