Show commands:
SageMath
E = EllipticCurve("gh1")
E.isogeny_class()
Elliptic curves in class 267696.gh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 267696.gh1 | 267696gh1 | \([0, 0, 0, -12192843, -16387225270]\) | \(55635379958596/24057\) | \(86682028706178048\) | \([2]\) | \(12644352\) | \(2.5925\) | \(\Gamma_0(N)\)-optimal |
| 267696.gh2 | 267696gh2 | \([0, 0, 0, -12132003, -16558854910]\) | \(-27403349188178/578739249\) | \(-4170619129169050601472\) | \([2]\) | \(25288704\) | \(2.9391\) |
Rank
sage: E.rank()
The elliptic curves in class 267696.gh have rank \(1\).
Complex multiplication
The elliptic curves in class 267696.gh do not have complex multiplication.Modular form 267696.2.a.gh
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.
