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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 235950z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
235950.z2 | 235950z1 | \([1, 1, 0, -46950, 3384000]\) | \(3307949/468\) | \(1619317476562500\) | \([2]\) | \(1382400\) | \(1.6443\) | \(\Gamma_0(N)\)-optimal |
235950.z1 | 235950z2 | \([1, 1, 0, -198200, -30647250]\) | \(248858189/27378\) | \(94730072378906250\) | \([2]\) | \(2764800\) | \(1.9909\) |
Rank
sage: E.rank()
The elliptic curves in class 235950z have rank \(1\).
Complex multiplication
The elliptic curves in class 235950z do not have complex multiplication.Modular form 235950.2.a.z
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.