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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 33640d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33640.g2 | 33640d1 | \([0, -1, 0, -9531, 338300]\) | \(10061824/725\) | \(6899950523600\) | \([2]\) | \(53760\) | \(1.2102\) | \(\Gamma_0(N)\)-optimal |
| 33640.g1 | 33640d2 | \([0, -1, 0, -30556, -1646460]\) | \(20720464/4205\) | \(640315408590080\) | \([2]\) | \(107520\) | \(1.5568\) |
Rank
sage: E.rank()
The elliptic curves in class 33640d have rank \(0\).
Complex multiplication
The elliptic curves in class 33640d do not have complex multiplication.Modular form 33640.2.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 Cremona 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 Cremona labels.
