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SageMath
E = EllipticCurve("cw1")
E.isogeny_class()
Elliptic curves in class 35490.cw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35490.cw1 | 35490ct4 | \([1, 1, 1, -63125, 6078197]\) | \(5763259856089/5670\) | \(27368007030\) | \([2]\) | \(147456\) | \(1.2961\) | |
| 35490.cw2 | 35490ct2 | \([1, 1, 1, -3975, 92217]\) | \(1439069689/44100\) | \(212862276900\) | \([2, 2]\) | \(73728\) | \(0.94948\) | |
| 35490.cw3 | 35490ct1 | \([1, 1, 1, -595, -3775]\) | \(4826809/1680\) | \(8109039120\) | \([2]\) | \(36864\) | \(0.60291\) | \(\Gamma_0(N)\)-optimal |
| 35490.cw4 | 35490ct3 | \([1, 1, 1, 1095, 317325]\) | \(30080231/9003750\) | \(-43459381533750\) | \([2]\) | \(147456\) | \(1.2961\) |
Rank
sage: E.rank()
The elliptic curves in class 35490.cw have rank \(0\).
Complex multiplication
The elliptic curves in class 35490.cw do not have complex multiplication.Modular form 35490.2.a.cw
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
