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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 235950.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
235950.x1 | 235950x2 | \([1, 1, 0, -84547905, 298927703925]\) | \(301832602552272335237/309456388859904\) | \(68527608713130048768000\) | \([2]\) | \(36495360\) | \(3.3000\) | |
235950.x2 | 235950x1 | \([1, 1, 0, -4010305, 6978903925]\) | \(-32209943913443717/76420466343936\) | \(-16922939722091200512000\) | \([2]\) | \(18247680\) | \(2.9535\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 235950.x have rank \(1\).
Complex multiplication
The elliptic curves in class 235950.x do not have complex multiplication.Modular form 235950.2.a.x
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.