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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 1287.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1287.d1 | 1287c2 | \([1, -1, 0, -117, -338]\) | \(244140625/61347\) | \(44721963\) | \([2]\) | \(256\) | \(0.17794\) | |
| 1287.d2 | 1287c1 | \([1, -1, 0, 18, -41]\) | \(857375/1287\) | \(-938223\) | \([2]\) | \(128\) | \(-0.16863\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1287.d have rank \(1\).
Complex multiplication
The elliptic curves in class 1287.d do not have complex multiplication.Modular form 1287.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
