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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 201586.e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 201586.e1 | 201586cf2 | \([1, 0, 1, -166136, 3114780]\) | \(2433138625/1387778\) | \(289243993795152242\) | \([2]\) | \(2150400\) | \(2.0403\) | |
| 201586.e2 | 201586cf1 | \([1, 0, 1, -106846, -13391556]\) | \(647214625/3332\) | \(694463370456548\) | \([2]\) | \(1075200\) | \(1.6937\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 201586.e have rank \(1\).
Complex multiplication
The elliptic curves in class 201586.e do not have complex multiplication.Modular form 201586.2.a.e
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.
