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SageMath
E = EllipticCurve("eu1")
E.isogeny_class()
Elliptic curves in class 190400eu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
190400.dx2 | 190400eu1 | \([0, -1, 0, 50367, -860863]\) | \(3449795831/2071552\) | \(-8485076992000000\) | \([2]\) | \(1228800\) | \(1.7457\) | \(\Gamma_0(N)\)-optimal |
190400.dx1 | 190400eu2 | \([0, -1, 0, -205633, -6748863]\) | \(234770924809/130960928\) | \(536415961088000000\) | \([2]\) | \(2457600\) | \(2.0923\) |
Rank
sage: E.rank()
The elliptic curves in class 190400eu have rank \(0\).
Complex multiplication
The elliptic curves in class 190400eu do not have complex multiplication.Modular form 190400.2.a.eu
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.