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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 4290w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4290.y4 | 4290w1 | \([1, 0, 0, 1094, -29980]\) | \(144794100308831/474439680000\) | \(-474439680000\) | \([4]\) | \(6144\) | \(0.92359\) | \(\Gamma_0(N)\)-optimal |
| 4290.y3 | 4290w2 | \([1, 0, 0, -10426, -354844]\) | \(125337052492018849/18404100000000\) | \(18404100000000\) | \([2, 2]\) | \(12288\) | \(1.2702\) | |
| 4290.y1 | 4290w3 | \([1, 0, 0, -160426, -24744844]\) | \(456612868287073618849/12544848030000\) | \(12544848030000\) | \([2]\) | \(24576\) | \(1.6167\) | |
| 4290.y2 | 4290w4 | \([1, 0, 0, -44746, 3289940]\) | \(9908022260084596129/1047363281250000\) | \(1047363281250000\) | \([2]\) | \(24576\) | \(1.6167\) |
Rank
sage: E.rank()
The elliptic curves in class 4290w have rank \(0\).
Complex multiplication
The elliptic curves in class 4290w do not have complex multiplication.Modular form 4290.2.a.w
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.
