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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 62866.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 62866.d1 | 62866c4 | \([1, 1, 0, -208975, 25321947]\) | \(159661140625/48275138\) | \(305164673538575762\) | \([2]\) | \(943488\) | \(2.0601\) | |
| 62866.d2 | 62866c3 | \([1, 1, 0, -190485, 31915481]\) | \(120920208625/19652\) | \(124227426638948\) | \([2]\) | \(471744\) | \(1.7135\) | |
| 62866.d3 | 62866c2 | \([1, 1, 0, -79545, -8666371]\) | \(8805624625/2312\) | \(14614991369288\) | \([2]\) | \(314496\) | \(1.5108\) | |
| 62866.d4 | 62866c1 | \([1, 1, 0, -5585, -101803]\) | \(3048625/1088\) | \(6877642997312\) | \([2]\) | \(157248\) | \(1.1642\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 62866.d have rank \(0\).
Complex multiplication
The elliptic curves in class 62866.d do not have complex multiplication.Modular form 62866.2.a.d
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
