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SageMath
sage: E = EllipticCurve("x1")
sage: E.isogeny_class()
Elliptic curves in class 424830x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
424830.x3 | 424830x1 | [1, 1, 0, -49858, 2684452] | [2] | 3538944 | \(\Gamma_0(N)\)-optimal |
424830.x2 | 424830x2 | [1, 1, 0, -333078, -72142272] | [2, 2] | 7077888 | |
424830.x4 | 424830x3 | [1, 1, 0, 91752, -243008898] | [2] | 14155776 | |
424830.x1 | 424830x4 | [1, 1, 0, -5289428, -4684521582] | [2] | 14155776 |
Rank
sage: E.rank()
The elliptic curves in class 424830x have rank \(0\).
Complex multiplication
The elliptic curves in class 424830x do not have complex multiplication.Modular form 424830.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.