Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 264d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 264.d1 | 264d1 | \([0, 1, 0, -8016, -278928]\) | \(55635379958596/24057\) | \(24634368\) | \([2]\) | \(336\) | \(0.76071\) | \(\Gamma_0(N)\)-optimal |
| 264.d2 | 264d2 | \([0, 1, 0, -7976, -281808]\) | \(-27403349188178/578739249\) | \(-1185257981952\) | \([2]\) | \(672\) | \(1.1073\) |
Rank
sage: E.rank()
The elliptic curves in class 264d have rank \(0\).
Complex multiplication
The elliptic curves in class 264d do not have complex multiplication.Modular form 264.2.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.
