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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 201810.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 201810.w1 | 201810cb4 | \([1, 0, 1, -358954, -82806034]\) | \(5763259856089/5670\) | \(5032145871270\) | \([2]\) | \(1843200\) | \(1.7306\) | |
| 201810.w2 | 201810cb2 | \([1, 0, 1, -22604, -1274794]\) | \(1439069689/44100\) | \(39138912332100\) | \([2, 2]\) | \(921600\) | \(1.3840\) | |
| 201810.w3 | 201810cb1 | \([1, 0, 1, -3384, 47542]\) | \(4826809/1680\) | \(1491006184080\) | \([2]\) | \(460800\) | \(1.0374\) | \(\Gamma_0(N)\)-optimal |
| 201810.w4 | 201810cb3 | \([1, 0, 1, 6226, -4296178]\) | \(30080231/9003750\) | \(-7990861267803750\) | \([2]\) | \(1843200\) | \(1.7306\) |
Rank
sage: E.rank()
The elliptic curves in class 201810.w have rank \(1\).
Complex multiplication
The elliptic curves in class 201810.w do not have complex multiplication.Modular form 201810.2.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 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.
