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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 3150.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3150.d1 | 3150q1 | \([1, -1, 0, -18117, -108459]\) | \(461889917/263424\) | \(375070500000000\) | \([2]\) | \(15360\) | \(1.4863\) | \(\Gamma_0(N)\)-optimal |
| 3150.d2 | 3150q2 | \([1, -1, 0, 71883, -918459]\) | \(28849701763/16941456\) | \(-24121721531250000\) | \([2]\) | \(30720\) | \(1.8329\) |
Rank
sage: E.rank()
The elliptic curves in class 3150.d have rank \(1\).
Complex multiplication
The elliptic curves in class 3150.d do not have complex multiplication.Modular form 3150.2.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.
