Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 139656f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 139656.x1 | 139656f1 | \([0, 1, 0, -4408, -34816]\) | \(62500/33\) | \(5002428761088\) | \([2]\) | \(201344\) | \(1.1283\) | \(\Gamma_0(N)\)-optimal |
| 139656.x2 | 139656f2 | \([0, 1, 0, 16752, -254880]\) | \(1714750/1089\) | \(-330160298231808\) | \([2]\) | \(402688\) | \(1.4749\) |
Rank
sage: E.rank()
The elliptic curves in class 139656f have rank \(0\).
Complex multiplication
The elliptic curves in class 139656f do not have complex multiplication.Modular form 139656.2.a.f
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.
