Show commands:
SageMath
E = EllipticCurve("cf1")
E.isogeny_class()
Elliptic curves in class 217800.cf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 217800.cf1 | 217800bl1 | \([0, 0, 0, -1034550, -390814875]\) | \(379275264/15125\) | \(4883363257781250000\) | \([2]\) | \(4423680\) | \(2.3525\) | \(\Gamma_0(N)\)-optimal |
| 217800.cf2 | 217800bl2 | \([0, 0, 0, 462825, -1428495750]\) | \(2122416/171875\) | \(-887884228687500000000\) | \([2]\) | \(8847360\) | \(2.6991\) |
Rank
sage: E.rank()
The elliptic curves in class 217800.cf have rank \(0\).
Complex multiplication
The elliptic curves in class 217800.cf do not have complex multiplication.Modular form 217800.2.a.cf
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.
