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SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 20286.ca
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20286.ca1 | 20286co2 | \([1, -1, 1, -267035, 49791179]\) | \(24553362849625/1755162752\) | \(150533500962724992\) | \([2]\) | \(258048\) | \(2.0430\) | |
| 20286.ca2 | 20286co1 | \([1, -1, 1, 15205, 3390923]\) | \(4533086375/60669952\) | \(-5203426444296192\) | \([2]\) | \(129024\) | \(1.6964\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 20286.ca have rank \(1\).
Complex multiplication
The elliptic curves in class 20286.ca do not have complex multiplication.Modular form 20286.2.a.ca
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
