Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 2842.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2842.a1 | 2842b2 | \([1, 0, 1, -1922982, 1025947640]\) | \(6684374974140996553/2097096248576\) | \(246721276548717824\) | \([2]\) | \(61440\) | \(2.3130\) | |
| 2842.a2 | 2842b1 | \([1, 0, 1, -104102, 20470776]\) | \(-1060490285861833/926330847232\) | \(-108981897845997568\) | \([2]\) | \(30720\) | \(1.9664\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2842.a have rank \(0\).
Complex multiplication
The elliptic curves in class 2842.a do not have complex multiplication.Modular form 2842.2.a.a
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.
