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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 4788.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4788.d1 | 4788c2 | \([0, 0, 0, -44679, 3634990]\) | \(52852623679312/8379\) | \(1563722496\) | \([2]\) | \(6144\) | \(1.1675\) | |
| 4788.d2 | 4788c1 | \([0, 0, 0, -2784, 57157]\) | \(-204589760512/2600283\) | \(-30329700912\) | \([2]\) | \(3072\) | \(0.82090\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4788.d have rank \(0\).
Complex multiplication
The elliptic curves in class 4788.d do not have complex multiplication.Modular form 4788.2.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.
